Raising an imaginary number to a higher power to simplify

The video tutorial explains how to calculate I to the 55th power by understanding the properties of the imaginary unit I, which is the square root of -1. The tutorial highlights the repeating pattern of powers of I, which cycles every four powers. By dividing 55 by 4, the remainder is found to be 3, indicating that I to the 55th is equivalent to I cubed, which equals negative I. The tutorial provides a clear step-by-step explanation of this process.

What is the value of i squared?

• 1

• -1

• i

• -i

How often do the powers of i repeat their pattern?

• Every 4 powers

• Every 3 powers

• Every 5 powers

• Every 2 powers

What is the remainder when 55 is divided by 4?

• 4

• 3

• 2

• 1

What is the value of i cubed?

• -1

• 1

• -i

• i

What is the final value of i to the 55th power?

• 1

• -1

• i

• -i