Problem
You need to perform complex algebra (e.g., when working on electrical engineering problems involving alternating current), and would like to know how Excel supports complex numbers so you can use them in your spreadsheets.
Solution
Excel supports complex numbers in the form a + bi or a + bj (j is often used to indicate a complex number instead of i, as is common in electrical engineering applications). Further, Excel provides 18 builtin functions that can be used to manipulate complex numbers and perform complex algebra.

Discussion
In Excel, a complex number is entered into a cell in the form a + bi or a + bj. In reality, Excel treats complex numbers entered this way as text. To enter a complex number, simply type it in as you would text. For example, to enter the complex number 6 + 2j, simply select a cell, type in 6+2j and then press Enter. Or you can use the COMPLEX function to let Excel format the complex number, given the real and imaginary parts you provide. For example, entering the formula =COMPLEX(6,2) in a cell results in the cell displaying the text 6+2i.
Excel provides a suite of specialpurpose imaginary number functions to manipulate complex numbers in these forms. There are 18 functions that are designed to work specifically with complex numbers. All but one of these functions start with the prefix IM (for example, IMABS, IMPRODUCT and so on). The one function that does not start with the IM prefix is COMPLEX. These and the other complex number functions are summarized in Table 78.
Function 
Syntax 
Description 

COMPLEX 
=COMPLEX(real part,imaginary part) 
Takes the real and imaginary arguments and returns text representing the complex number 
IMABS 
=IMABS(complex number) 
Returns the modulus of the complex number 
IMAGINARY 
=IMAGINARY(complex number) 
Returns the imaginary part of a complex number 
IMARGUMENT 
=IMARGUMENT(complex number) 
Returns the argument Q, in radians, of the complex number, where Q is from the exponential form of complex numbers, reiQ 
IMCONJUGATE 
=IMCONJUGATE(complex number) 
Returns the complex conjugate of a complex number 
IMCOS 
=IMCOS(complex number) 
Returns the cosine of a complex number 
IMDIV 
=IMDIV(n1, n2) 
Returns the quotient of two complex numbers where the first argument is the numerator and the second is the denominator 
IMEXP 
=IMEXP(complex number) 
Returns the exponential of a complex number 
IMLN 
=IMLN(complex number) 
Returns the natural logarithm of a complex number 
IMLOG10 
=IMLOG10(complex number) 
Returns the base 10 logarithm of a complex number 
IMLOG2 
=IMLOG2(complex number) 
Returns the base 2 logarithm of a complex number 
IMPOWER 
=IMPOWER(complex number, n) 
Raises the complex number to the nth power 
IMPRODUCT 
=IMPRODUCT(n1, n2, n3, ...) 
Returns the product of two or more complex numbers 
IMREAL 
=IMREAL(complex number) 
Returns the real part of a complex number 
IMSIN 
=IMSIN(complex number) 
Returns the sine of a complex number 
IMSQRT 
=IMSQRT(complex number) 
Returns the square root of a complex number 
IMSUB 
=IMSUB(n1, n2) 
Subtracts the complex number n2 from n1 
IMSUM 
=IMSUM(n1, n2, n3, ...) 
Returns the sum of two or more complex numbers 
Using Excel
Getting Acquainted with Visual Basic for Applications
Collecting and Cleaning Up Data
Charting
Statistical Analysis
Time Series Analysis
Mathematical Functions
Curve Fitting and Regression
Solving Equations
Numerical Integration and Differentiation
Solving Ordinary Differential Equations
Solving Partial Differential Equations
Performing Optimization Analyses in Excel
Introduction to Financial Calculations
Index