imaginary numbers

Front

What is an imaginary number?

Back

An imaginary number is a complex 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

How do you multiply two imaginary numbers?

Back

To multiply two imaginary numbers, multiply their coefficients and apply the property i^2 = -1. For example, (-3i)(4i) = -12i^2 = 12.

Front

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

Back

(3i)(2i) = 6i^2 = -6.

Front

What is the sum of i and 6i?

Back

i + 6i = 7i.

Front

How do you simplify the expression (-3i)(i)(5i)?

Back

(-3i)(i)(5i) = -15i^3 = 15i.

Front

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

Back

(3 - i) - (2 + 4i) = 1 - 5i.

Front

What is the product of (-3i)(4i)(-5i)?

Back

(-3i)(4i)(-5i) = -60i.

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 real part of the complex number 3 + 4i?

Back

The real part is 3.