Complex Number Test Review

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 i = √(-1).

Front

What is the imaginary unit 'i'?

Back

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

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

Front

Calculate the square of the complex number (1 - 7i).

Back

(1 - 7i)^2 = 1^2 - 2(1)(7i) + (7i)^2 = 1 - 14i - 49 = -48 - 14i.

Front

Find the sum of the complex numbers (5 - 2i) and (-7 + 8i).

Back

(5 - 2i) + (-7 + 8i) = (5 - 7) + (-2i + 8i) = -2 + 6i.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

What is the value of i^3?

Back

i^3 = i^2 * i = -1 * i = -i.

Front

What is the value of i^4?

Back

i^4 = (i^2)^2 = (-1)^2 = 1.

Front

What is the value of i^5?

Back

i^5 = i^4 * i = 1 * i = i.

Front

What is the value of i^6?

Back

i^6 = i^4 * i^2 = 1 * -1 = -1.