IMSUM

Returns the sum of complex numbers.

Syntax:

IMSUM(complexnum1, complexnum2, ... complexnum29)

complexnum1, complexnum2, ... are complex numbers as text, or references to cells / cell ranges containing complex numbers as text.

Example:

IMSUM("1+2i", "3+4i")

returns 4+6i as text.

IMSUM(A1:A2)

where cell A1 contains the text 1+2i and cell A2 contains 3+4i, returns 4+6i as text.

Application:

Electrical Circuit Analysis

Imagine you're an electrical engineer working on a circuit. You have several components connected in series, and you need to find the total impedance of the circuit. Impedance is a measure of the opposition to the flow of alternating current and is represented by a complex number, where the real part is the resistance and the imaginary part is the reactance.

Let's say you have three components with the following impedances:

Z1=4+2i (Resistance of 4Ω, Reactance of 2Ω)
Z2=3−5i (Resistance of 3Ω, Reactance of −5Ω)
Z3=2+7i (Resistance of 2Ω, Reactance of 7Ω)

To find the total impedance of the circuit, you simply add the impedances of each component. Manually, you would add the real parts and the imaginary parts separately:

Total Impedance = (4+3+2)+(2−5+7)i=9+4i

Using a spreadsheet, you can use the IMSUM function to perform this calculation automatically.

Here's how you could set up the data in a table:

	Component	Impedance (Z)
	A	B
1	Z1	4+2i
2	Z2	3-5i
3	Z3	2+7i
4	Total Impedance	IMSUM(B1:B3)

By entering the formula IMSUM(B1:B3) in cell B4, the spreadsheet will calculate the sum of the complex numbers in the specified range. The result displayed in cell B4 will be 9+4i, which is the total impedance of the circuit. This saves you from having to manually separate and sum the real and imaginary parts, reducing the chance of error and making the calculation much more efficient.