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 the square root of -1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as 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 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

How do you find the powers of i?

Back

The powers of i cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1, and then it repeats.

Front

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

Back

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

Front

How do you multiply two complex numbers (a + bi)(c + di)?

Back

(a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

Front

What is the result of (2 - 3i)(5 + 4i)?

Back

(2 - 3i)(5 + 4i) = 22 - 7i.

Front

What is the value of i^7?

Back

i^7 = -i.