Complex Numbers

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, 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 represent the square root of negative numbers.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL method) and combine like terms, remembering that i² = -1.

Front

What is the result of (3i)(-2 + 4i)?

Back

-12 - 6i.

Front

How do you simplify the expression (4 + 7i) - (3 + 2i)?

Back

Combine like terms: (4 - 3) + (7i - 2i) = 1 + 5i.

Front

What is the simplified form of -4√-63?

Back

-12i√7.

Front

What is the product of (2i)(3i)?

Back

-6.

Front

How do you simplify √-108?

Back

√-108 = √(108) * √(-1) = 6i√3.

Front

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

Back

The conjugate 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.