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 — a complex number of the form x + yi

COMPLEX(x,y,i)

x: real part

y: imaginary part

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

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

This function is Excel compatible.

IMABS — the absolute value of the complex number z

IMABS(z)

z: a complex number

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

This function is Excel compatible.

IMAGINARY, IMREAL.

IMAGINARY — the imaginary part of the complex number z

IMAGINARY(z)

z: a complex number

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

This function is Excel compatible.

IMREAL.

IMARCCOS — the complex arccosine of the complex number

IMARCCOS(z)

z: a complex number

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.

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

IMARCSIN, IMARCTAN.

IMARCCOSH — the complex hyperbolic arccosine of the complex number z

IMARCCOSH(z)

z: a complex number

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

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

IMARCSINH, IMARCTANH.

IMARCCOT — the complex arccotangent of the complex number z

IMARCCOT(z)

z: a complex number

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

IMARCSEC, IMARCCSC.

IMARCCOTH — the complex hyperbolic arccotangent of the complex number z

IMARCCOTH(z)

z: a complex number

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

IMARCSECH, IMARCCSCH.

IMARCCSC — the complex arccosecant of the complex number z

IMARCCSC(z)

z: a complex number

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

IMARCSEC, IMARCCOT.

IMARCCSCH — the complex hyperbolic arccosecant of the complex number z

IMARCCSCH(z)

z: a complex number

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

IMARCSECH, IMARCCOTH.

IMARCSEC — the complex arcsecant of the complex number z

IMARCSEC(z)

z: a complex number

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

IMARCCSC, IMARCCOT.

IMARCSECH — the complex hyperbolic arcsecant of the complex number z

IMARCSECH(z)

z: a complex number

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

IMARCCSCH, IMARCCOTH.

IMARCSIN — the complex arcsine of the complex number z

IMARCSIN(z)

z: a complex number

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.

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

IMARCCOS, IMARCTAN.

IMARCSINH — the complex hyperbolic arcsine of the complex number z

IMARCSINH(z)

z: a complex number

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

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

IMARCCOSH, IMARCTANH.

IMARCTAN — the complex arctangent of the complex number

IMARCTAN(z)

z: a complex number

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

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

IMARCSIN, IMARCCOS.

IMARCTANH — the complex hyperbolic arctangent of the complex number z

IMARCTANH(z)

z: a complex number

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.

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

IMARCSINH, IMARCCOSH.

IMARGUMENT — the argument theta of the complex number z

IMARGUMENT(z)

z: a complex number

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

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 — the complex conjugate of the complex number z

IMCONJUGATE(z)

z: a complex number

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

This function is Excel compatible.

IMAGINARY, IMREAL.

IMCOS — the cosine of the complex number z

IMCOS(z)

z: a complex number

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

This function is Excel compatible.

IMSIN, IMTAN.

IMCOSH — the hyperbolic cosine of the complex number z

IMCOSH(z)

z: a complex number

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

IMSINH, IMTANH.

IMCOT — the cotangent of the complex number z

IMCOT(z)

z: a complex number

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

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

IMSEC, IMCSC.

IMCOTH — the hyperbolic cotangent of the complex number z

IMCOTH(z)

z: a complex number

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

IMSECH, IMCSCH.

IMCSC — the cosecant of the complex number z

IMCSC(z)

z: a complex number

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

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

IMSEC, IMCOT.

IMCSCH — the hyperbolic cosecant of the complex number z

IMCSCH(z)

z: a complex number

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

IMSECH, IMCOTH.

IMDIV — the quotient of two complex numbers z1/z2

IMDIV(z1,z2)

z1: a complex number

z2: a complex number

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

This function is Excel compatible.

IMPRODUCT.

IMEXP — the exponential of the complex number z

IMEXP(z)

z: a complex number

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

This function is Excel compatible.

IMLN.

IMFACT — the factorial of the complex number z

IMFACT(z)

z: a complex number

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

IMGAMMA.

IMGAMMA — the gamma function of the complex number z

IMGAMMA(z)

z: a complex number

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

IMGAMMA.

IMIGAMMA — the incomplete Gamma function

IMIGAMMA(a,z,lower,regularize)

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

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

GAMMA, IMIGAMMA.

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

IMINV(z)

z: a complex number

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

IMLN — the natural logarithm of the complex number z

IMLN(z)

z: a complex number

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.

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

This function is Excel compatible.

IMEXP, IMLOG2, IMLOG10.

IMLOG10 — the base-10 logarithm of the complex number z

IMLOG10(z)

z: a complex number

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

This function is Excel compatible.

IMLN, IMLOG2.

IMLOG2 — the base-2 logarithm of the complex number z

IMLOG2(z)

z: a complex number

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

This function is Excel compatible.

IMLN, IMLOG10.

IMNEG — the negative of the complex number z

IMNEG(z)

z: a complex number

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

IMPOWER — the complex number z1 raised to the z2th power

IMPOWER(z1,z2)

z1: a complex number

z2: a complex number

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

This function is Excel compatible.

IMSQRT.

IMPRODUCT — the product of the given complex numbers

IMPRODUCT(z1,z2,…)

z1: a complex number

z2: a complex number

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

This function is Excel compatible.

IMDIV.

IMREAL — the real part of the complex number z

IMREAL(z)

z: a complex number

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

This function is Excel compatible.

IMAGINARY.

IMSEC — the secant of the complex number z

IMSEC(z)

z: a complex number

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

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

IMCSC, IMCOT.

IMSECH — the hyperbolic secant of the complex number z

IMSECH(z)

z: a complex number

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

IMCSCH, IMCOTH.

IMSIN — the sine of the complex number z

IMSIN(z)

z: a complex number

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

This function is Excel compatible.

IMCOS, IMTAN.

IMSINH — the hyperbolic sine of the complex number z

IMSINH(z)

z: a complex number

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

IMCOSH, IMTANH.

IMSQRT — the square root of the complex number z

IMSQRT(z)

z: a complex number

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

This function is Excel compatible.

IMPOWER.

IMSUB — the difference of two complex numbers

IMSUB(z1,z2)

z1: a complex number

z2: a complex number

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

This function is Excel compatible.

IMSUM.

IMSUM — the sum of the given complex numbers

IMSUM(z1,z2,…)

z1: a complex number

z2: a complex number

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

This function is Excel compatible.

IMSUB.

IMTAN — the tangent of the complex number z

IMTAN(z)

z: a complex number

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

This function is Excel compatible.

IMSIN, IMCOS.

IMTANH — the hyperbolic tangent of the complex number z

IMTANH(z)

z: a complex number

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

IMSINH, IMCOSH.

Complex

COMPLEX

Synopsis

Arguments

Note

Microsoft Excel Compatibility

IMABS

Synopsis

Arguments

Note

Microsoft Excel Compatibility

See also

IMAGINARY

Synopsis

Arguments

Note

Microsoft Excel Compatibility

See also

IMARCCOS

Synopsis

Arguments

Description

Note

See also

IMARCCOSH

Synopsis

Arguments

Description

Note

See also

IMARCCOT

Synopsis

Arguments

Note

See also

IMARCCOTH

Synopsis

Arguments

Note

See also

IMARCCSC

Synopsis

Arguments

Note

See also

IMARCCSCH

Synopsis

Arguments

Note

See also

IMARCSEC

Synopsis

Arguments

Note

See also

IMARCSECH

Synopsis

Arguments

Note

See also

IMARCSIN

Synopsis

Arguments

Description

Note

See also

IMARCSINH

Synopsis

Arguments

Description

Note

See also

IMARCTAN

Synopsis

Arguments

Description

Note

See also

IMARCTANH

Synopsis