Imaginary & Complex Numbers

Front

What is 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 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

The value of i^2 is -1.

Front

How do you add two complex numbers?

Back

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

Front

Calculate: (1 − 2i) + (-4 + 2i)

Back

The result is -3.

Front

Calculate: (5 - 2i) + (-7 + 8i)

Back

The result is -2 + 6i.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL method) and combine like terms, remembering that i^2 = -1.

Front

Multiply: (1 − 2i)(6 + 5i)

Back

The result is 16 − 7i.

Front

What is the product of two imaginary numbers, (2i)(3i)?

Back

The product is -6.

Front

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

Back

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