COMPLEX Function

Summary

COMPLEX builds a complex number from separate real and imaginary parts. If your worksheet stores those parts in different cells, this function turns them into one valid complex value such as 3+4i or 50+30j.

This matters because Excel's complex-number functions work with complex values as text in a specific format. COMPLEX gives you a clean way to create that format instead of typing the string by hand every time.

COMPLEX matters because many of Excel's engineering functions expect a properly formed complex-number input rather than two separate numeric pieces. By assembling those parts into one valid value, COMPLEX becomes the entry point that makes the rest of the IM* family work smoothly.

That also makes it useful in models where the real and imaginary components are calculated in different cells. Instead of typing complex text manually, the workbook can build it from live numeric inputs, which is safer, easier to maintain, and much clearer when the underlying numbers change.

Syntax

=COMPLEX(real_num, i_num, [suffix])

The formula has two required numeric parts and one optional notation choice. real_num supplies the value on the real axis, i_num supplies the coefficient of the imaginary unit, and suffix tells Excel whether to write the result with i or j.

For example, =COMPLEX(3,4) returns 3+4i, while =COMPLEX(3,4,"j") returns 3+4j. The numeric value is the same in both cases. Only the displayed notation changes.

One useful detail is that COMPLEX builds the text format expected by Excel's IM functions. That means the result can be passed directly into formulas such as IMSUM, IMSUB, IMREAL, or IMAGINARY without extra cleanup.

Arguments

• real_num - [required] The real part of the complex number.
• i_num - [required] The imaginary part of the complex number.
• [suffix] - [optional] The imaginary suffix to use. Excel accepts "i" or "j". If omitted, Excel uses "i".

real_num and i_num are usually ordinary numbers or cell references. They do not need to be text. Excel combines them into one valid complex-number result, so a formula like =COMPLEX(B1,B2) works naturally when the two components are stored in separate worksheet cells.

suffix is optional, but it matters for notation consistency. In mathematics, i is the usual symbol for the imaginary unit. In electrical engineering, j is often preferred because i may already represent current. Excel allows either one, but it does not accept other suffixes.

It is also worth noting how zero values affect the result. If i_num is 0, Excel can return a purely real-looking value such as 10. If real_num is 0, the result can be purely imaginary, such as 2i or 2j. The formula is still producing a valid complex-number result in both cases.

COMPLEX vs similar functions

COMPLEX is for creating a complex value, while the IM functions usually calculate with one:

Using COMPLEX

The main use is building a valid complex value from separate inputs. That is helpful when the real and imaginary parts are already stored in different cells and you want to pass the result into another complex-number formula such as IMSUM or IMSUB.

The optional suffix matters when your worksheet needs j instead of i. Excel supports both, but you should stay consistent within the same workflow so your formulas are easier to read and maintain.

COMPLEX can also return results that look simpler than you might expect. If the imaginary part is 0, Excel can return just the real number as a complex value. If the real part is 0, the result can be purely imaginary, like 2i.

Example 1 - Build 3+4i

This is the standard use of COMPLEX: take a real component and an imaginary component from separate inputs and assemble them into one valid complex value. Here, 3 is the real part and 4 is the imaginary part, so Excel returns 3+4i.

This is useful because many engineering formulas in Excel expect one complex number as input, not two separate cells. The example shows how to build that combined value first so later IM functions can work with it correctly.

=COMPLEX(3, 4) // Returns "3+4i"

Example 2 - Build a value with j

The mathematics is the same as the previous example, but the notation changes from i to j. With real part 50 and imaginary part 30, Excel returns 50+30j.

This matters in engineering contexts where j is the preferred symbol for the imaginary unit, especially in circuit work where i might already mean current. So the example is not changing the math, only the way the result is written.

=COMPLEX(50, 30, "j") // Returns "50+30j"

Example 3 - Keep the imaginary part at zero

A complex-number workflow does not stop being useful just because one side is zero. This formula uses real part 10 and imaginary part 0, so Excel returns 10.

The result looks like a normal number, but the example still matters because it lets the sheet keep using the same complex-number workflow. You do not need a different formula just because the imaginary side happens to be zero in this case.

=COMPLEX(10, 0) // Returns "10"

Example 4 - Create a pure imaginary value

When the real component is zero, Excel returns a purely imaginary result such as 2i. In this example, the real part is 0 and the imaginary part is 2, so the entire value sits on the imaginary side.

This helps when the worksheet needs to represent a value that has no real component but still has to stay in a valid complex-number format. It shows beginners that COMPLEX can build full mixed values, real-only values, and imaginary-only values with the same function.

=COMPLEX(0, 2) // Returns "2i"

Conclusion Recap

COMPLEX is the function that assembles a valid Excel complex number from separate parts. In this lesson, that meant taking one real value and one imaginary value and turning them into a single result that other engineering functions can understand and use.

That is what makes COMPLEX so useful as a starting point. Instead of typing complex-number text by hand, you can build it from cell values and formulas more safely. Once the real and imaginary parts are packaged correctly, the rest of the IM* functions become much easier to work with.

• Builds a complex value: COMPLEX combines separate real and imaginary parts.
• Supports i or j: Use the optional suffix when you need a specific notation.
• Returns complex text: The result is ready for other IM functions.
• Works well with cell-based inputs: It is especially useful when the two parts start in different cells.
• Handles zero parts cleanly: The result can be purely real or purely imaginary when one side is zero.