The Excel IMPOWER function returns a complex number raised to a given power. The complex number must be in the form x + yi or x + yj. Use the COMPLEX function to create a complex number from real and imaginary parts
Syntax:= IMPOWER (inumber, number)
The IMPOWER function syntax has the following arguments:
- Inumber: Required. A complex number you want to raise to a power.
-
Number: Required. The power to which you want to raise the complex number
Example: Let’s look at some Excel IMPOWER function examples and explore how to use the IMPOWER function as a worksheet function in Microsoft Excel:
Syntax: =IMPOWER(A2,B2)
Result:
Based on the Excel spreadsheet above, the following IMPOWER examples would return:
Syntax: =IMPOWER(A3,B3)
Result: -11+2i
Syntax: =IMPOWER(A4,B4)
Result: -7+24i
Syntax: =IMPOWER(A5,B5)
Result: 1
Syntax: =IMPOWER(A6,B6)
Result: 64
Syntax: =IMPOWER(A7,B7)
Result: -119+120i
Syntax: =IMPOWER(A8,B8)
Result: -115+236i
Syntax: =IMPOWER(A9,B9)
Result: -236+115i
Syntax: =IMPOWER(A10,B10)
Result: -85-132i
Syntax: =IMPOWER(A11,B11)
Result: -119-120i
Syntax: =IMPOWER(A12,B12)
Result: 7+24j
Syntax: =IMPOWER(A13,B13)
Result: 24+10i
Note:
-
Use COMPLEX to convert real and imaginary coefficients into a complex number.
- If number is nonnumeric, IMPOWER returns the #VALUE! error value.
- Number can be an integer, fractional, or negative.
-
A complex number raised to a power is calculated as follows:
where: 
and: 
and: 
