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 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 conjugate of a complex number a + bi?

Back

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

Front

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

Back

To multiply two complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi². Since i² = -1, this simplifies to (ac - bd) + (ad + bc)i.

Front

What is the result of (4 + 3i)(4 - 3i)?

Back

The result is 25.

Front

What is the result of i^7?

Back

The result is -i.

Front

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

Back

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

Front

What is the result of (1 - 2i) + (-4 + 2i)?

Back

The result is -3.

Front

How do you subtract two complex numbers (a + bi) - (c + di)?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts: (a - c) + (b - d)i.

Front

What is the result of (10 + 15i) - (48 - 30i)?

Back

The result is -38 + 45i.