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

i^2 = -1.

Front

What is the value of i^3?

Back

i^3 = i^2 * i = -1 * i = -i.

Front

What is the value of i^4?

Back

i^4 = (i^2)^2 = (-1)^2 = 1.

Front

How do you simplify √-1?

Back

√-1 = i.

Front

How do you simplify √-x where x > 0?

Back

√-x = i√x.

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.

Front

What is the value of i^79?

Back

i^79 = i^(4*19 + 3) = (i^4)^19 * i^3 = 1^19 * -i = -i.

Front

How do you simplify √-45?

Back

√-45 = √(-1 * 45) = √-1 * √45 = i√45 = 3i√5.

Front

What is the value of i^126?

Back

i^126 = i^(4*31 + 2) = (i^4)^31 * i^2 = 1^31 * -1 = -1.