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# A to Z of Excel Functions: The IMAGINARY Function

6 July 2020

Welcome back to our regular A to Z of Excel Functions blog. Today we look at the IMAGINARY function.

The IMAGINARY function

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit (sometimes denoted j) which is defined by its property i2 = −1.  In general, the square of an imaginary number bi is −b2.  For example, 9i is an imaginary number, and its square is −81.  Zero is considered to be both real and imaginary.

An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers a and b are called, respectively, the real part and the imaginary part of the complex number.

The IMAGINARY function really does exist, and it returns the imaginary coefficient of a complex number in the form a + bi.

The IMAGINARY function employs the following syntax to operate:

IMAGINARY(inumber)

The IMAGINARY function has the following argument:

• inumber: this is required and represents the complex number for which you want the imaginary coefficient.

It should be further noted that:

• you should use COMPLEX to convert real and imaginary coefficients into a complex number
• IMAGINARY recognises either the i or j notation
• if the complex number ends in +i or -i (or j), i.e. there is no coefficient between the operator and the imaginary unit, there must be no space, otherwise IMAGINARY will return an #NUM! error.