Algebra 2 - How do you simplify a complex number to a high power i^ 31

The video tutorial explains the concept of the imaginary unit i, starting with its definition as the square root of -1. It covers the calculation of i squared, i cubed, and higher powers, highlighting the repeating pattern every four exponents. The tutorial introduces modular arithmetic as a method to simplify calculations of higher powers of i, using division to find remainders and determine the equivalent power. The video concludes with a discussion on shortcuts for calculating powers of i efficiently.

What is the value of i squared?

• 1

• i

• -1

• 0

What is the result of i cubed?

• i

• -i

• 1

• -1

What does i to the fourth power equal?

• i

• -i

• 1

• -1

How often does the cycle of powers of i repeat?

• Every 4 exponents

• Every 3 exponents

• Every 2 exponents

• Every 5 exponents

What is the remainder when 31 is divided by 4?

• 0

• 3

• 1

• 2

What is i to the 31st power equivalent to?

• i

• -1

• -i

• 1

Which mathematical concept helps simplify calculations of higher powers of i?

• Subtraction

• Addition

• Modular Arithmetic

• Exponential Growth