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# A to Z of Excel Functions: The IMSUB Function

18 January 2021

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

The IMSUB 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 might wish to subtract one complex number from another.  IMSUB returns the difference of two complex numbers in the x + yi or x + yj text format.

The IMSUB function employs the following syntax to operate:

IMSUB(inumber1, inumber2)

The IMSUB function has the following arguments:

• inumber1: the first argument and represents the number from which to subtract number2
• inumber2: this is also required.  This is the complex number to subtract from inumber1.

It should be further noted that:

• you should use COMPLEX to convert real and imaginary coefficients into a complex number
• IMSUB recognises either the i or j notation
• if any of inumber1 or inumber2 is a value that is not in the x + yi or x + yj text format, IMSUB returns the #NUM! error value
• if any of inumber1 or inumber2 is a logical value, IMSUB returns the #VALUE! error value
• if any of inumber1 or inumber2 is non-numeric, IMSUB returns the #VALUE! error value
• if any 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 IMSUB will return an #NUM! error
• the difference of two complex numbers is given by:  