PreAlgebra II Final Exam Complex Numbers Review!

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 i² = -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 multiply two complex numbers?

Back

To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi². Remember that i² = -1.

Front

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

Back

The result is 11 - 10i.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used to simplify the division of complex numbers.

Front

How do you add complex numbers?

Back

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

Front

What is the result of (-3 + 4i)(6 - 5i)?

Back

The result is 2 + 39i.

Front

What is the result of -3i ∙ -4i (-7 - i)?

Back

The result is 84 + 12i.

Front

How do you simplify √-25?

Back

√-25 can be simplified to 5i, since √-1 = i.

Front

What is i raised to the power of 23?

Back

i^23 = -i.