The IMPOWER function in Google Sheets is a powerful and versatile tool designed for handling complex numbers. It allows users to raise a complex number to a specified power, facilitating advanced mathematical computations, particularly in fields such as engineering and physics.

Syntax

IMPOWER(complex_number, exponent) 

• complex_number: The complex number you want to raise to a power. It can be provided in the form of a string (e.g., “2+3i”) or as separate real and imaginary parts.
• exponent: The power to which the complex number is raised. This can be any real or complex number.

Example #1

IMPOWER("3+4i", 2) 

This example raises the complex number 3 + 4i to the power of 2. The result would be -7 + 24i, calculated as follows: (3 + 4i)² = 9 + 24i – 16 = -7 + 24i.

Example #2

IMPOWER("1+2i", 3) 

In this case, the complex number 1 + 2i is raised to the power of 3. This computes to -11 + 6i, derived from multiplying (1 + 2i) three times.

Example #3

IMPOWER("2", 4) 

Here, the function raises the real number 2 to the power of 4. The result is 16, as it involves simply multiplying 2 by itself four times: 2 2 2 2 = 16.

Error handling

• VALUE! This error occurs when the complex number is not formatted correctly, meaning it cannot be interpreted by the function.
• NUM! This error arises when the exponent is not a valid number or when a calculation results in an invalid operation, such as raising a complex number to an imaginary exponent.
• N/A! This error appears if the complex number or exponent is missing, indicating that the function requires both parameters to compute a result.

Conclusion

The IMPOWER function in Google Sheets is an essential tool for those working with complex numbers, allowing intricate calculations to be performed with relative ease. By raising complex numbers to specified powers, users can unlock a range of mathematical possibilities, catering to both practical and theoretical applications.