Intro to 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.

Front

What does the imaginary unit 'i' represent?

Back

The imaginary unit 'i' represents the square root of -1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

How do you simplify the expression √-4?

Back

√-4 = 2i.

Front

What is the general form of a complex number?

Back

The general form of a complex number is a + bi, where a is the real part and b is the imaginary part.

Front

What is the value of i^3?

Back

i^3 = -i.

Front

What is the value of i^4?

Back

i^4 = 1.

Front

How do you find i^n for any integer n?

Back

To find i^n, divide n by 4 and use the remainder to determine the value: 0 -> 1, 1 -> i, 2 -> -1, 3 -> -i.

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 add two complex numbers?

Back

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