Imaginary 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 the value of i^2?

Back

i^2 = -1.

Front

Multiply: (2-5i)(2+5i)

Back

29.

Front

Simplify √-45

Back

3i√5.

Front

Simplify: (10+ 15i)-(48 - 30i)

Back

-38 + 45i.

Front

Simplify 2√-32

Back

8i√2.

Front

What is the principal square root of -1?

Back

i.

Front

What is the standard form of a complex number?

Back

A complex number is in standard form when expressed as a + bi, where a and b are real numbers.

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL) and apply the fact that i^2 = -1.