# IMPOWER function

The `IMPOWER` function returns a complex number raised to a power.

### Parts of a IMPOWER formula

The `IMPOWER` formula is formatted as `=IMPOWER(complex_base, exponent).`

 Part Description Notes `complex_base` The complex number to raise to the exponent power. May be written as a ∓ bi or a ∓ bj. `exponent` The exponent to raise complex_base to. Must be a number.

### Sample formulas

`IMPOWER("4-3i",0.5)`

`IMPOWER(A2,B2)`

`IMPOWER("2j",-7)`

### Notes

• The exponentiation of a complex number is defined as follows:
• (a+bi)n = rn(cosθ + isinθ), where
• r = √(x2 + y2) and θ = arctan(b/a)

### Examples

A B
1 Formula Result
2 `=IMPOWER("5+2i", 3)` 65+142i
3 `=IMPOWER("-1-j", -1)` -0.5+0.5j
4 `=IMPOWER("0.732-5.349i", -0.138)` 0.776914096672106+0.155872432042838i

### Related functions

`COMPLEX`: The COMPLEX function creates a complex number, given real and imaginary coefficients.

`IMREAL`: Returns the real coefficient of a complex number.

`IMAGINARY`: Returns the imaginary coefficient of a complex number.

`POWER`: Returns a number raised to a power.