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 the square root of -1. It is used to extend the real number system to include solutions to equations that do not have real solutions.

Front

How do you add complex numbers?

Back

To add complex numbers, combine their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Front

What is the result of (8 + 2i) + (1 - 6i) - (-8 - 8i)?

Back

The result is 17 + 4i.

Front

What is the product of (3 - 2i) and (7 + 6i)?

Back

The product is 33 + 4i.

Front

What is the simplified form of (-3 + 2i)(1 - 4i)?

Back

The simplified form is 5 + 14i.

Front

What is the result of (10 + 3i) - (2 - 9i)?

Back

The result is 8 + 12i.

Front

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

Back

The product is -3.

Front

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

Back

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