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# A to Z of Excel Functions: The IMDIV Function

14 September 2020

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

The IMDIV 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.

Sometimes you wish to divide one imaginary number (inumber1), z1 = a + bi, by another (inumber2), z2 = c + di.  The IMDIV function can help you do this (i.e. z1 / z2).

The IMDIV function employs the following syntax to operate:

IMDIV(inumber1, inumber2)

The IMDIV function has the following arguments:

• inumber1: this is required and represents the numerator of the required division
• inumber2: this is required and represents the denominator of the required division.

It should be further noted that:

• you should use >COMPLEX to convert real and imaginary coefficients into a complex number
• IMDIV recognises either the i or j notation
• if inumber1 or inumber2 is a value that is not in the x + yi or x + yj text format, IMDIV returns the #NUM! error value
• if inumber1 or inumber2 is a logical value, IMDIV returns the #VALUE! error value
• 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 IMDIV will return an #NUM! error
• The quotient of the two complex numbers is calculated as