Imaginary Numbers Flashcard

Front

What are imaginary numbers?

Back

Imaginary numbers are numbers 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 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

The value of i^2 is -1.

Front

Calculate: (1 − 2i) + (-4 + 2i)

Back

-3.

Front

Calculate: (2i)(3i)

Back

-6.

Front

What is the result of multiplying two imaginary numbers?

Back

The result of multiplying two imaginary numbers is a real number.

Front

Simplify: -3i(4 + 2i)

Back

6 - 12i.

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 complex numbers?

Back

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

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL) and combine like terms.