10.3 Complex functions in EXCEL Now, let’s look at the list in Table 10-1. This shows the 18 complex functions in

EXCEL. We’ll examine the usage, syntax, and some examples of these functions.

Table 10-1. Complex Functions in EXCEL

COMPLEX IMABS IMAGINARY IMARGUMENT

IMCONJUGATE IMCOS IMDIV IMEXP

IMLN IMLOG10 IMLOG2 IMPOWER

IMPRODUCT IMREAL IMSIN IMSQRT

IMSUB IMSUM

COMPLEX This transforms real and imaginary coefficients into a complex number of the

form x + yi or x + yj.

Syntax: COMPLEX(real_num,i_num,suffix)

Suffix must be i or j. Don’t use upper case!

Examples: COMPLEX(3,4) equals 3 + 4i

COMPLEX(3,4,"j") equals 3 + 4j

COMPLEX(0,1) equals i

COMPLEX(1,0) equals 1

IMABS Returns the absolute value (modulus) of a complex number in x + yi or x + yj text

format.

Syntax: IMABS(inumber)

inumber is a complex number for which you want the absolute value.

Example: IMABS("3+4i") equals 5. Note that "3+4i" is in text form, not numeric

form. Complex numbers are not numerics in EXCEL.

IMAGINARY Returns the imaginary coefficient of a complex number in x + yi or x + yj text

format.

Syntax: IMAGINARY(inumber)

inumber is a complex number for which you want the imaginary coefficient.

Examples: IMAGINARY("3+4i") equals 4

IMAGINARY("0-j") equals -1 10.3 Complex functions in Excel 10-7

IMAGINARY(4) equals 0

IMARGUMENT

Returns the argument (), an angle expressed in radians. Syntax: IMARGUMENT(inumber)

inumber is a complex number for which you want the argument . Example: IMARGUMENT("3+4i") equals 0.927295

IMCONJUGATE Returns the complex conjugate of a complex number in x + yi or x + yj text format.

All complex numbers are in text format.

Syntax: IMCONJUGATE(inumber)

inumber is a complex number for which you want the conjugate.

Example: IMCONJUGATE("3+4i") equals 3–4i

IMCOS Returns the cosine of a complex number in x + yi or x + yj text format.

Syntax: IMCOS(inumber)

inumber is a complex number for which you want the cosine.

Example: IMCOS("1+i") equals 0.83373 - 0.988898i

(Note that the cosine of a complex number is complex.)

IMDIV Returns the quotient of two complex numbers in x + yi or x + yj text format.

Syntax: IMDIV(inumber1,inumber2)

inumber1 is the complex numerator or dividend.

inumber2 is the complex denominator or divisor.

Example: IMDIV("-238+240i","10+24i") equals 5 + 12i

IMEXP Returns the exponential of a complex number in x + yi or x + yj text format.

Syntax: IMEXP(inumber)

inumber is a complex number for which you want the exponential.

Example: IMEXP("1+i") equals 1.468694 + 2.287355i

IMLN Returns the natural logarithm of a complex number in x + yi or x + yj text format.

Syntax: IMLN(inumber)

inumber is a complex number for which you want the natural logarithm.

Example: IMLN("3+4i") equals 1.609438 + 0.927295I

IMLOG10 Returns the common logarithm (base 10) of a complex number in x + yi or 10-8 Chapter 10: Complex Math

x + yj text format.

Syntax: IMLOG10(inumber)

inumber is a complex number for which you want the common logarithm.

Example: IMLOG10("3+4i") equals 0.69897 + 0.402719i

IMLOG2 Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.

Syntax: IMLOG2(inumber)

inumber is a complex number for which you want the base-2 logarithm.

Example: IMLOG2("3+4i") equals 2.321928 + 1.337804i

IMPOWER Returns a complex number in x + yi or x + yj text format raised to a power.

Syntax IMPOWER(inumber,number)

inumber is a complex number you want to raise to a power.

number is the power to which you want to raise the complex number.

Example: IMPOWER("2+3i", 3) equals –4 6 + 9i

IMPRODUCT Returns the product of 2 to 29 complex numbers in x + yi or x + yj text format.

Syntax: IMPRODUCT(inumber1,inumber2,...)

inumber1, inumber2,… are 1 to 29 complex numbers to multiply.

Examples: IMPRODUCT("3+4i","5-3i") equals 27 + 11i

IMPRODUCT("1+2i",30) equals 30 + 60i

IMREAL Returns the real coefficient of a complex number in x + yi or x + yj text format.

Syntax: IMREAL(inumber)

inumber is a complex number for which you want the real coefficient.

Example: IMREAL("10-9i") equals 6

IMSIN Returns the sine of a complex number in x + yi or x + yj text format.

Syntax: IMSIN(inumber)

inumber is a complex number for which you want the sine.

Example: IMSIN("3+4i") equals 3.853738 – 2 7.016813i

IMSQRT Returns the square root of a complex number in x + yi or x + yj text format.

Syntax: IMSQRT(inumber)

inumber is a complex number for which you want the square root.

Example: IMSQRT("1+i") equals 1.098684 + 0.45509I 10.4 Graphing a complex function 10-9

IMSUB Returns the difference of two complex numbers in x + yi or x + yj text format.

Syntax: IMSUB(inumber1,inumber2)

inumber1 is the complex number from which to subtract inumber2.

inumber2 is the complex number to subtract from inumber1.

Example: IMSUB("13+4i","5+3i") equals 8 + i

IMSUM Returns the sum of two or more complex numbers in x + yi or x + yj text format.

Syntax: IMSUM(inumber1,inumber2,...)

inumber1,inumber2,...are 1 to 29 complex numbers to add.

Example: IMSUM("3+4i","5-3i") equals 8 + i

From EXECL for Engineers and Scientists, S.C.Bloch, 2nd edition, Wiley Press