Imaginary and Complex Numbers

Front

What is the definition of an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

Front

What is the definition of 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 value of i^2?

Back

i^2 = -1.

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

Calculate: i + 2i

Back

3i.

Front

Calculate: (2 + 3i) + (4 + 5i)

Back

6 + 8i.

Front

Calculate: (1 + 2i) - (3 - 4i)

Back

-2 + 6i.

Front

What is the conjugate of the complex number 3 + 4i?

Back

The conjugate is 3 - 4i.

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.