Imaginary Numbers

Front

What is an imaginary number?

Back

An imaginary number is a complex 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

i^2 = -1.

Front

What is the pattern of powers of i?

Back

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

Front

Simplify i^13.

Back

i^13 = i.

Front

What is the square root of a negative number?

Back

Front

Solve for x: x^2 = -121.

Back

x = ±11i.

Front

What is the value of i^79?

Back

i^79 = -i.

Front

Back

Front

What is the solution to the equation x^2 + 36 = 0?

Back

x = ±6i.

Front

What is the imaginary unit 'i' used for?

Back

The imaginary unit 'i' is used to extend the real number system to include solutions to equations that do not have real solutions, such as x^2 + 1 = 0.