N.7 - Complex Numbers

Front

Simplify: -2(6 - 2i)

Back

-12 + 4i

Front

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

Back

13

Front

Simplify: (2 - 5i)(4 + i)

Back

13 - 18i

Front

Simplify: (-2 + i)²

Back

3 - 4i

Front

Simplify: (i)⁹

Back

i

Front

Define complex number.

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Front

What is the imaginary unit i?

Back

The imaginary unit i is defined as the square root of -1.

Front

What is the conjugate of a complex number a + bi?

Back

The conjugate of a complex number a + bi is a - bi.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL) and combine like terms, remembering that i² = -1.

Front

What is the result of (a + bi)(a - bi)?

Back

The result is a² + b².