Complex Numbers

Front

What is a 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, defined as i² = -1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1. It is used to extend the real number system to include solutions to equations that do not have real solutions.

Front

How do you simplify √-1?

Back

√-1 = i.

Front

What is the process to simplify √-a?

Back

To simplify √-a, you can express it as i√a, where a is a positive real number.

Front

Simplify: √-108

Back

6i√3.

Front

Simplify: √-25

Back

5i.

Front

What is the result of adding two complex numbers (a + bi) and (c + di)?

Back

(a + c) + (b + d)i.

Front

What is the result of subtracting two complex numbers (a + bi) - (c + di)?

Back

(a - c) + (b - d)i.

Front

Simplify: -4√-63

Back

-12i√7.

Front

Simplify: 2i - 7i + 10

Back

-5i + 10.