Complex

  • COMPLEX a complex number of the form x + yi
  • IMABS the absolute value of the complex number z
  • IMAGINARY the imaginary part of the complex number z
  • IMARCCOS the complex arccosine of the complex number
  • IMARCCOSH the complex hyperbolic arccosine of the complex number z
  • IMARCCOT the complex arccotangent of the complex number z
  • IMARCCOTH the complex hyperbolic arccotangent of the complex number z
  • IMARCCSC the complex arccosecant of the complex number z
  • IMARCCSCH the complex hyperbolic arccosecant of the complex number z
  • IMARCSEC the complex arcsecant of the complex number z
  • IMARCSECH the complex hyperbolic arcsecant of the complex number z
  • IMARCSIN the complex arcsine of the complex number z
  • IMARCSINH the complex hyperbolic arcsine of the complex number z
  • IMARCTAN the complex arctangent of the complex number
  • IMARCTANH the complex hyperbolic arctangent of the complex number z
  • IMARGUMENT the argument theta of the complex number z
  • IMCONJUGATE the complex conjugate of the complex number z
  • IMCOS the cosine of the complex number z
  • IMCOSH the hyperbolic cosine of the complex number z
  • IMCOT the cotangent of the complex number z
  • IMCOTH the hyperbolic cotangent of the complex number z
  • IMCSC the cosecant of the complex number z
  • IMCSCH the hyperbolic cosecant of the complex number z
  • IMDIV the quotient of two complex numbers z1/z2
  • IMEXP the exponential of the complex number z
  • IMFACT the factorial of the complex number z
  • IMGAMMA the gamma function of the complex number z
  • IMIGAMMA the incomplete Gamma function
  • IMINV the reciprocal, or inverse, of the complex number z
  • IMLN the natural logarithm of the complex number z
  • IMLOG10 the base-10 logarithm of the complex number z
  • IMLOG2 the base-2 logarithm of the complex number z
  • IMNEG the negative of the complex number z
  • IMPOWER the complex number z1 raised to the z2th power
  • IMPRODUCT the product of the given complex numbers
  • IMREAL the real part of the complex number z
  • IMSEC the secant of the complex number z
  • IMSECH the hyperbolic secant of the complex number z
  • IMSIN the sine of the complex number z
  • IMSINH the hyperbolic sine of the complex number z
  • IMSQRT the square root of the complex number z
  • IMSUB the difference of two complex numbers
  • IMSUM the sum of the given complex numbers
  • IMTAN the tangent of the complex number z
  • IMTANH the hyperbolic tangent of the complex number z

COMPLEX

COMPLEX a complex number of the form x + yi

Synopsis

COMPLEX(x,y,i)

Arguments

x: real part

y: imaginary part

i: the suffix for the complex number, either "i" or "j"; defaults to "i"

Note

If i is neither "i" nor "j", COMPLEX returns #VALUE!

Microsoft Excel Compatibility

This function is Excel compatible.

IMABS

IMABS the absolute value of the complex number z

Synopsis

IMABS(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMAGINARY, IMREAL.

IMAGINARY

IMAGINARY the imaginary part of the complex number z

Synopsis

IMAGINARY(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMREAL.

IMARCCOS

IMARCCOS the complex arccosine of the complex number

Synopsis

IMARCCOS(z)

Arguments

z: a complex number

Description

IMARCCOS returns the complex arccosine of the complex number z. The branch cuts are on the real axis, less than -1 and greater than 1.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSIN, IMARCTAN.

IMARCCOSH

IMARCCOSH the complex hyperbolic arccosine of the complex number z

Synopsis

IMARCCOSH(z)

Arguments

z: a complex number

Description

IMARCCOSH returns the complex hyperbolic arccosine of the complex number z. The branch cut is on the real axis, less than 1.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSINH, IMARCTANH.

IMARCCOT

IMARCCOT the complex arccotangent of the complex number z

Synopsis

IMARCCOT(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSEC, IMARCCSC.

IMARCCOTH

IMARCCOTH the complex hyperbolic arccotangent of the complex number z

Synopsis

IMARCCOTH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSECH, IMARCCSCH.

IMARCCSC

IMARCCSC the complex arccosecant of the complex number z

Synopsis

IMARCCSC(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSEC, IMARCCOT.

IMARCCSCH

IMARCCSCH the complex hyperbolic arccosecant of the complex number z

Synopsis

IMARCCSCH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSECH, IMARCCOTH.

IMARCSEC

IMARCSEC the complex arcsecant of the complex number z

Synopsis

IMARCSEC(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCCSC, IMARCCOT.

IMARCSECH

IMARCSECH the complex hyperbolic arcsecant of the complex number z

Synopsis

IMARCSECH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCCSCH, IMARCCOTH.

IMARCSIN

IMARCSIN the complex arcsine of the complex number z

Synopsis

IMARCSIN(z)

Arguments

z: a complex number

Description

IMARCSIN returns the complex arcsine of the complex number z. The branch cuts are on the real axis, less than -1 and greater than 1.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCCOS, IMARCTAN.

IMARCSINH

IMARCSINH the complex hyperbolic arcsine of the complex number z

Synopsis

IMARCSINH(z)

Arguments

z: a complex number

Description

IMARCSINH returns the complex hyperbolic arcsine of the complex number z. The branch cuts are on the imaginary axis, below -i and above i.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCCOSH, IMARCTANH.

IMARCTAN

IMARCTAN the complex arctangent of the complex number

Synopsis

IMARCTAN(z)

Arguments

z: a complex number

Description

IMARCTAN returns the complex arctangent of the complex number z. The branch cuts are on the imaginary axis, below -i and above i.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSIN, IMARCCOS.

IMARCTANH

IMARCTANH the complex hyperbolic arctangent of the complex number z

Synopsis

IMARCTANH(z)

Arguments

z: a complex number

Description

IMARCTANH returns the complex hyperbolic arctangent of the complex number z. The branch cuts are on the real axis, less than -1 and greater than 1.

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMARCSINH, IMARCCOSH.

IMARGUMENT

IMARGUMENT the argument theta of the complex number z

Synopsis

IMARGUMENT(z)

Arguments

z: a complex number

Description

The argument theta of a complex number is its angle in radians from the real axis.

Note

If z is not a valid complex number, #VALUE! is returned. If z is 0, 0 is returned. This is different from Excel which returns an error.

IMCONJUGATE

IMCONJUGATE the complex conjugate of the complex number z

Synopsis

IMCONJUGATE(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMAGINARY, IMREAL.

IMCOS

IMCOS the cosine of the complex number z

Synopsis

IMCOS(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSIN, IMTAN.

IMCOSH

IMCOSH the hyperbolic cosine of the complex number z

Synopsis

IMCOSH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSINH, IMTANH.

IMCOT

IMCOT the cotangent of the complex number z

Synopsis

IMCOT(z)

Arguments

z: a complex number

Description

IMCOT(z) = IMCOS(z)/IMSIN(z).

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSEC, IMCSC.

IMCOTH

IMCOTH the hyperbolic cotangent of the complex number z

Synopsis

IMCOTH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSECH, IMCSCH.

IMCSC

IMCSC the cosecant of the complex number z

Synopsis

IMCSC(z)

Arguments

z: a complex number

Description

IMCSC(z) = 1/IMSIN(z).

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSEC, IMCOT.

IMCSCH

IMCSCH the hyperbolic cosecant of the complex number z

Synopsis

IMCSCH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSECH, IMCOTH.

IMDIV

IMDIV the quotient of two complex numbers z1/z2

Synopsis

IMDIV(z1,z2)

Arguments

z1: a complex number

z2: a complex number

Note

If z1 or z2 is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMPRODUCT.

IMEXP

IMEXP the exponential of the complex number z

Synopsis

IMEXP(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMLN.

IMFACT

IMFACT the factorial of the complex number z

Synopsis

IMFACT(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMGAMMA.

IMGAMMA

IMGAMMA the gamma function of the complex number z

Synopsis

IMGAMMA(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMGAMMA.

IMIGAMMA

IMIGAMMA the incomplete Gamma function

Synopsis

IMIGAMMA(a,z,lower,regularize)

Arguments

a: a complex number

z: a complex number

lower: if true (the default), the lower incomplete gamma function, otherwise the upper incomplete gamma function

regularize: if true (the default), the regularized version of the incomplete gamma function

Note

The regularized incomplete gamma function is the unregularized incomplete gamma function divided by gamma(a).

See also

GAMMA, IMIGAMMA.

IMINV

IMINV the reciprocal, or inverse, of the complex number z

Synopsis

IMINV(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

IMLN

IMLN the natural logarithm of the complex number z

Synopsis

IMLN(z)

Arguments

z: a complex number

Description

The result will have an imaginary part between -π and +π.

The natural logarithm is not uniquely defined on complex numbers. You may need to add or subtract an even multiple of π to the imaginary part.

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMEXP, IMLOG2, IMLOG10.

IMLOG10

IMLOG10 the base-10 logarithm of the complex number z

Synopsis

IMLOG10(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMLN, IMLOG2.

IMLOG2

IMLOG2 the base-2 logarithm of the complex number z

Synopsis

IMLOG2(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMLN, IMLOG10.

IMNEG

IMNEG the negative of the complex number z

Synopsis

IMNEG(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

IMPOWER

IMPOWER the complex number z1 raised to the z2th power

Synopsis

IMPOWER(z1,z2)

Arguments

z1: a complex number

z2: a complex number

Note

If z1 or z2 is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSQRT.

IMPRODUCT

IMPRODUCT the product of the given complex numbers

Synopsis

IMPRODUCT(z1,z2,…)

Arguments

z1: a complex number

z2: a complex number

Note

If any of z1, z2,... is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMDIV.

IMREAL

IMREAL the real part of the complex number z

Synopsis

IMREAL(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMAGINARY.

IMSEC

IMSEC the secant of the complex number z

Synopsis

IMSEC(z)

Arguments

z: a complex number

Description

IMSEC(z) = 1/IMCOS(z).

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMCSC, IMCOT.

IMSECH

IMSECH the hyperbolic secant of the complex number z

Synopsis

IMSECH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMCSCH, IMCOTH.

IMSIN

IMSIN the sine of the complex number z

Synopsis

IMSIN(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMCOS, IMTAN.

IMSINH

IMSINH the hyperbolic sine of the complex number z

Synopsis

IMSINH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMCOSH, IMTANH.

IMSQRT

IMSQRT the square root of the complex number z

Synopsis

IMSQRT(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMPOWER.

IMSUB

IMSUB the difference of two complex numbers

Synopsis

IMSUB(z1,z2)

Arguments

z1: a complex number

z2: a complex number

Note

If z1 or z2 is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSUM.

IMSUM

IMSUM the sum of the given complex numbers

Synopsis

IMSUM(z1,z2,…)

Arguments

z1: a complex number

z2: a complex number

Note

If any of z1, z2,... is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSUB.

IMTAN

IMTAN the tangent of the complex number z

Synopsis

IMTAN(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

Microsoft Excel Compatibility

This function is Excel compatible.

See also

IMSIN, IMCOS.

IMTANH

IMTANH the hyperbolic tangent of the complex number z

Synopsis

IMTANH(z)

Arguments

z: a complex number

Note

If z is not a valid complex number, #VALUE! is returned.

See also

IMSINH, IMCOSH.