IMPOWER Google Sheet Formula

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IMPOWER Formula Syntax

=IMPOWER("3+4i", 2)

Example Use Case

Raising a complex number to a power

Understanding the IMPOWER Formula

The IMPOWER function in Excel returns a complex number raised to a power. It's an advanced mathematical tool for complex number operations—like computing multiple rotations, exponential growth, or iterative applications of complex transformations.

IMPOWER("3+4i", 2) returns the complex number "3+4i" squared, which equals (3²-4²) + (2×3×4)i. It takes a complex number argument in text form ("x+yi" or "x+yj") and a numeric power, calculating the result according to complex number rules—valuable for applications in engineering, physics, or mathematics requiring complex exponentiation.

Why Use IMPOWER?

IMPOWER enables complex exponentiation—think waveform analysis or multiple rotations in the complex plane. Its implementation of complex number powers follows the mathematical identity z^n = r^n × e^(in𝜃), making it essential for many advanced calculations in science and engineering.

Example with Sample Data

Complex Number, Power	Formula	Result
"3+4i", 2	=IMPOWER("3+4i", 2)	-7+24i
"i", 4	=IMPOWER("i", 4)	1
"2+2i", 0.5	=IMPOWER("2+2i", 0.5)	1.5537739740300+0.6435942529055i

IMPOWER calculates complex powers: (3+4i)² equals -7+24i, i⁴ equals 1 (demonstrating the cyclic nature of i's powers), and the square root of 2+2i (power 0.5) gives approximately 1.55+0.64i. It's a complex exponentiation calculator.