Complex Numbers

Front

How do you write a complex number?

Back

A complex number is written in the form a + bi, where a is the real part and b is the imaginary part.

Front

Simplify √-23

Back

The simplification of √-23 is i√23.

Front

Express \(\sqrt{-225}\) in terms of \(i\)

Back

\(\sqrt{-225} = 15i\)

Front

What does i² equal?

Back

i² = -1.

Front

What letter represents an imaginary number?

Back

The letter 'i' represents an imaginary number.

Front

What is the real part of a complex number a + bi?

Back

The real part of a complex number a + bi is 'a'.

Front

What is the imaginary part of a complex number a + bi?

Back

The imaginary part of a complex number a + bi is 'b'.

Front

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

Back

To add two complex numbers, add the real parts and the imaginary parts: (a + c) + (b + d)i.

Front

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

Back

To multiply two complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi² = (ac - bd) + (ad + bc)i.

Front

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

Back

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