10.3 Complex functions in E XCEL - Milwaukee Area Technical ...

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 IMCONJUGATE IMLN IMPRODUCT IMSUB

IMABS IMCOS IMLOG10 IMREAL IMSUM

IMAGINARY IMDIV IMLOG2 IMSIN

IMARGUMENT IMEXP IMPOWER IMSQRT

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

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