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

Solve for x: x^2 + 36 = 0

Back

x = ±6i.

Front

Solve for x: ⅖(x + 3)² + 8 = -32

Back

x = -3 ± 10i.

Front

Solve for x: 2(x - 8)² + 40 = 16

Back

x = 8 ± 2i√3.

Front

Solve for x: 33 = 18 - 3x²

Back

x = ±i√5.

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

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 two complex numbers?

Back

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

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi)(c + di), use the distributive property and combine like terms: ac + adi + bci + bdi².