Real and Imaginary Numbers

Front

Define Real Numbers.

Back

Real numbers include all the numbers on the number line, including both rational numbers (like integers and fractions) and irrational numbers (like √2 and π).

Front

Define Imaginary Numbers.

Back

Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as √-1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which means i² = -1.

Front

Simplify: 2i(4 - 3i)

Back

6 + 8i

Front

What is the square root of a negative number?

Back

The square root of a negative number can be expressed in terms of 'i'. For example, √-x = i√x.

Front

Simplify: √-4

Back

2i

Front

What is the result of adding two complex numbers?

Back

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

Front

Calculate: (1 − 2i) + (-4 + 2i)

Back

-3

Front

Define 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.

Front

What is the conjugate of a complex number?

Back

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