Complex Numbers Review

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i = ?

√-1

Find the Quotient (2 + 3i)/(4 - 2i)

(1 + 8i)/10

i³ = ?

- √- 1 or just: - i

i² = ?

-1

simplify i⁴²

-1

i squared

-1 (negative 1 or minus 1)

Write the complex number in Standard Form (√-4)² - 7

-11

Find the sum √-4 + (-4 - √-4)

-4

Write the complex number in Standard Form √-9 - 5

-5 + 3i

i cubed

-i

simplify i²⁷

-i

i to the fourth

1

i⁴ = ?

1

simplify i⁸

1

Find the product. (2 - i)(4 + 3i)

11 + 2i

Find the product. (5 - 3i)²

16 - 30i

Find the product. 8i(4 - 3i)

24 + 32i

Write the complex number in Standard Form -3i² + i

3 +i

Write the complex number in Standard Form -√-12 + 3

3 -2i√3

Find the product. (3 - 5i)(3 + 5i)

34

Find the sum (3 - i) + (2 + 3i)

5 + 2i

Simplify 4i - (-3 + 5i) + (2 - 6i)

5 - 7i

Find the Quotient -5/2i

5i/2

What is a complex number?

A number that has both a real portion and an imaginary portion to it. Such as a + bi a is real but b is being multiplied by the imaginary unit and is thus imaginary

Rational Numbers

Can be expressed exactly as a ratio of two integers

Irrational Numbers

Cannot be expressed exactly as a ratio of two integers, but are real numbers

Real Numbers

Have points on the number line

Complex Numbers

Have the form a+bi, where a and b are real, and i=√ -1

Radicals

Involve square root, cube root, etc. of integers

If i is raised to any multiple of 4 such as: i⁸, i¹², i¹⁶, .....i⁴ⁿ then?

It still equals 1 just like i⁴

How are complex numbers multiplied?

Just like regular numbers and variables. Final answer however should not have any power of i higher than 1.

How are complex numbers divided?

Multiply the numerator and the denominator of the fraction by the conjugate of the denominator

Imaginary Numbers

Square roots of negative numbers. Have no points on the number line

Integers

Whole numbers and their opposites

When adding and subtracting complex numbers what is the rule?

You can only add/subtract reals numbers with real numbers and imaginary number with imaginary numbers.

i to the fifth

i

simplify i³⁷

i

i

the square root of negative 1 ie.√ -1


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