Simplifying Imaginary Numbers

Front

What is an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

Front

What is the value of i^2?

Back

-1

Front

What is the value of i^3?

Back

-i

Front

What is the value of i^4?

Back

1

Front

How do you simplify the expression i^n for n = 5?

Back

i^5 = i^(4+1) = i^4 * i = 1 * i = i.

Front

What is the pattern in the powers of i?

Back

The powers of i cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1.

Front

Solve for x: x² + 12 = 5

Back

x = ± i√7

Front

What is the value of i^129?

Back

i

Front

What is the value of i^{61}?

Back

i

Front

What is the value of i^{25}?

Back

i