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 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^79

Back

-i.

Front

What is the product of two imaginary numbers?

Back

The product of two imaginary numbers can be a real number. For example, (ai)(bi) = -ab.

Front

Simplify: (3i)(-2 + 4i)

Back

-12 - 6i.

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately.

Front

Simplify: (10 + 15i) - (48 - 30i)

Back

-38 + 45i.

Front

What is the result of subtracting complex numbers?

Back

Subtract the real parts and the imaginary parts separately.

Front

Simplify: 2i - 7i + 10

Back

10 - 5i.