# Excel Complex Arithmetic Function Summary

```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
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,&quot;j&quot;) 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(&quot;3+4i&quot;) equals 5. Note that &quot;3+4i&quot; 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(&quot;3+4i&quot;) equals 4
IMAGINARY(&quot;0-j&quot;) 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(&quot;3+4i&quot;) equals 0.927295
IMARGUMENT
IMEXP
IMPOWER
IMSQRT
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(&quot;3+4i&quot;) 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(&quot;1+i&quot;) 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(&quot;-238+240i&quot;,&quot;10+24i&quot;) 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(&quot;1+i&quot;) 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(&quot;3+4i&quot;) 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(&quot;3+4i&quot;) 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(&quot;3+4i&quot;) 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(&quot;2+3i&quot;, 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(&quot;3+4i&quot;,&quot;5-3i&quot;) equals 27 + 11i
IMPRODUCT(&quot;1+2i&quot;,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(&quot;10-9i&quot;) 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(&quot;3+4i&quot;) 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(&quot;1+i&quot;) 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(&quot;13+4i&quot;,&quot;5+3i&quot;) 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(&quot;3+4i&quot;,&quot;5-3i&quot;) equals 8 + i
From EXECL for Engineers and Scientists, S.C.Bloch, 2nd edition, Wiley Press
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