Pre-Calculus - Rewriting complex numbers to higher powers

The video tutorial explores the concept of the imaginary unit i and its powers. It demonstrates how to calculate and simplify powers of i, revealing a repeating pattern every four powers. The tutorial explains the importance of understanding this pattern for simplifying higher powers of i using modulo 4. Practical examples are provided to illustrate the application of this pattern, emphasizing the use of division and remainders to simplify complex expressions involving powers of i.

What is the result of i squared?

• i

• -1

• 1

• -i

What does i to the fourth power equal?

• -i

• 1

• -1

• i

How often does the pattern of powers of i repeat?

• Every 5 powers

• Every 4 powers

• Every 2 powers

• Every 3 powers

How can you simplify i to the 13th power?

• -1

• -i

• i

• 1

What is the remainder when dividing 47 by 4, and what does it tell us about i to the 47th power?

• Remainder 2, i to the 47th is -1

• Remainder 1, i to the 47th is i

• Remainder 0, i to the 47th is 1

• Remainder 3, i to the 47th is -i