IMPRODUCT Google Sheet Formula

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IMPRODUCT Formula Syntax

=IMPRODUCT("3+4i", "2-i")

Example Use Case

Multiplying complex numbers together

Understanding the IMPRODUCT Formula

The IMPRODUCT function in Excel returns the product of two or more complex numbers. It's a mathematical tool for complex number operations—like performing multiplication in electrical engineering, quantum physics, or signal processing calculations.

IMPRODUCT("3+4i", "2-i") returns the result of multiplying the complex numbers "3+4i" and "2-i". It can take multiple complex number arguments in the form of text ("x+yi" or "x+yj"), performing complex multiplication according to the distributive property—valuable for advanced scientific or engineering applications involving complex quantities.

Why Use IMPRODUCT?

IMPRODUCT enables complex multiplication—think wave interference calculations or transformations in the complex plane. Its ability to correctly multiply multiple complex numbers saves time and prevents errors in fields where complex arithmetic is common, handling the process of distributing terms and combining like parts.

Example with Sample Data

Complex Numbers	Formula	Result
"3+4i" × "2-i"	=IMPRODUCT("3+4i", "2-i")	10+5i
"i" × "i"	=IMPRODUCT("i", "i")	-1
"2+i" × "3+2i" × "1-i"	=IMPRODUCT("2+i", "3+2i", "1-i")	9+i

IMPRODUCT performs complex multiplication: (3+4i)(2-i) equals 10+5i, i² equals -1 (the fundamental complex number identity), and the product of three complex numbers demonstrates the function's ability to handle multiple inputs. It's a complex multiplication calculator.