Algebra 2 - How to simplify an imaginary number to a higher power i^35

The video tutorial explains how to calculate powers of the imaginary unit i, focusing on i to the 35th power. It begins by demonstrating the step-by-step process to find i to the 5th and 6th powers, highlighting the repeating pattern every four powers. The instructor then introduces a shortcut using division to simplify the calculation of higher powers, specifically i to the 35th, by finding the remainder when dividing the exponent by 4. The tutorial concludes by simplifying i to the 35th as negative i.

What is the value of i to the 4th power?

• 0

• 1

• -1

• i

How is i to the 5th power related to i?

• i to the 5th is 0

• i to the 5th is 1

• i to the 5th is i

• i to the 5th is -i

What is the value of i to the 6th power?

• 0

• 1

• -1

• i

What is the remainder when 35 is divided by 4, and how does it help in finding i to the 35th power?

• Remainder is 2, i to the 35th is -1

• Remainder is 0, i to the 35th is 1

• Remainder is 3, i to the 35th is -i

• Remainder is 1, i to the 35th is i

What is the equivalent of i to the 35th power?

• -1

• i

• -i

• 1