Imaginary and Complex 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 definition of 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.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

What is the value of i^4?

Back

i^4 = 1.

Front

How do you find the complex conjugate of a complex number?

Back

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

Front

What is the complex conjugate of 4 - 3i?

Back

The complex conjugate is 4 + 3i.

Front

Simplify i^66.

Back

i^66 = -1.

Front

Simplify i^13.

Back

i^13 = i.

Front

How do you simplify the square root of a negative number, such as \sqrt{-18}?

Back

\sqrt{-18} = \sqrt{18} \cdot \sqrt{-1} = 3i\sqrt{2}.

Front

What is the result of dividing (2 - 4i) by (1 + 3i)?

Back

(2 - 4i)/(1 + 3i) = -1 - i.