Simplifying 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.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i^2 = -1.

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 i^2 = -1.

Front

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

Back

The result is -12 - 6i.

Front

How do you add two complex numbers?

Back

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

Front

What is the result of adding (3 + 2i) and (4i + 6)?

Back

The result is 9 + 6i.

Front

How do you multiply (7 + 2i)(9 - 6i)?

Back

Use the distributive property: (7)(9) + (7)(-6i) + (2i)(9) + (2i)(-6i) = 63 - 42i + 18i - 12i^2 = 75 - 24i.

Front

What is the simplified form of 3√-81?

Back

The simplified form is 27i.

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 divide two complex numbers?

Back

To divide two complex numbers, multiply the numerator and denominator by the conjugate of the denominator and simplify.