IMSUM Function

Summary

IMSUM adds complex numbers in Excel. It works with values written in the usual complex-number text format like "3+4i" or "5-2j", and it returns the result in the same kind of format.

This is useful when you are working with impedance, phasors, or signal math and you want Excel to add the real and imaginary parts for you. Instead of breaking everything into separate columns, you can keep the values as complex numbers and sum them directly.

IMSUM is practical because it keeps complex-number addition readable. Instead of decomposing each input into separate real and imaginary totals, the workbook can add full complex values directly and keep the result in the same valid format for another engineering step or final display.

Syntax

=IMSUM(inumber1, [inumber2], ...)

You give IMSUM one or more complex numbers, and Excel returns their total. For example, =IMSUM("3+4i","1+2i") returns 4+6i. Excel supports from 1 to 255 complex-number arguments here.

The pattern is straightforward: pass in the complex values you want to total, and Excel combines the real parts and imaginary parts for you. That makes IMSUM a convenient rollup function when several complex values need to be added in one place.

Arguments

• inumber1 - [required] The first complex number to add.
• [inumber2, ...] - [optional] More complex numbers to add, up to 255 total arguments.

Each input should be a valid Excel complex number, either typed as text or created with COMPLEX(). When several complex numbers appear in the same formula, it is best to keep the notation consistent and not mix i and j.

IMSUM vs similar functions

IMSUM is part of Excel's complex-number family, but each related function has a different job:

Using IMSUM

The most common use for IMSUM is simple: you already have complex values and you need the total. In an engineering worksheet, that might mean adding impedances in series or combining phasors from multiple sources. Excel handles the real and imaginary math together, so you do not need separate formulas for each part.

There are two format rules worth remembering. First, the inputs need to be valid complex numbers, usually written as text like "3+4i" or created with COMPLEX(). Second, keep the suffixes consistent. Excel accepts i and j, but not uppercase I or J. In practice, if you are adding several complex values, it is safest to stick to one suffix style across the formula.

One more practical point: IMSUM returns a complex text value, not a plain number. That is perfect if the result will be passed into another IM function, but if you only need one part afterward, use IMREAL or IMAGINARY on the result.

Example 1 - Add two complex numbers

This example shows the essential behavior of IMSUM. Excel adds the real coefficients together and adds the imaginary coefficients together, returning one combined complex result. That is much cleaner than splitting the values apart first and rebuilding the answer manually afterward.

Here, 3+4i plus 1+2i becomes 4+6i. It is a simple starting example that makes the add-both-parts rule easy to see.

=IMSUM("3+4i", "1+2i") // Returns "4+6i"

Example 2 - Add several impedance values

This pattern fits series-style engineering calculations where each component already exists as a complex value. Rather than summing resistance and reactance in separate steps, IMSUM produces the total complex impedance directly, which keeps the worksheet closer to the way the calculation is usually described conceptually.

This is useful because the learner can focus on the full result instead of managing separate helper formulas. The example shows how several complex parts can be combined in one clean step.

=IMSUM("5+2j", "10-1j", "3j") // Returns "15+4j"

Example 3 - Mix a real number with an imaginary value

This example shows that the inputs do not all need to be written in the same visual form. A plain real number and a purely imaginary value can still be added into one valid complex result. That makes IMSUM useful when the worksheet starts with separate real and imaginary contributions instead of already assembled complex strings.

So the example is helpful for beginners who may have numbers coming from different cells in different forms. IMSUM still combines them into one proper complex value without extra setup.

=IMSUM(10, "5i") // Returns "10+5i"

Example 4 - Add the same complex value repeatedly

Repeated addition is common when the same contribution appears multiple times in a model. Here, IMSUM totals the same complex value four times and returns the accumulated result. That makes the scaling effect visible on both the real and imaginary sides at once.

This example is good for showing growth by repetition. The learner can see that both parts scale together, so the final result keeps the same overall shape while getting larger.

=IMSUM("2+2i", "2+2i", "2+2i", "2+2i") // Returns "8+8i"

Conclusion Recap

IMSUM is the complex-number version of ordinary addition. In this lesson, that meant combining multiple complex values while keeping both the real and imaginary sides together in one valid result, instead of splitting the math into separate manual steps.

That is why IMSUM is useful in larger engineering-style models. As long as the inputs are valid complex values, Excel handles the addition and returns the total in the same complex format, ready for another IM* function or for display as the final answer.

• Adds complex numbers: IMSUM returns the total of two or more complex values.
• Works with 1 to 255 inputs: Useful for both short formulas and larger rollups.
• Returns text in complex format: The result comes back as something like 4+6i.
• Keep suffixes consistent: Use matching i or j values, and avoid uppercase versions.
• Pairs well with COMPLEX: Build inputs with COMPLEX() when your real and imaginary parts live in separate cells.