Multiplying and Dividing Complex Numbers

​Multiplying Complex Numbers

​When multiplying complex numbers, we use the FOIL Method like we did with polynomials.

​Example 1

Simplify the expression: (8+i)(2+7i)

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​First: 8(2) = 16

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​Outer: 8(7i) = 56i

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​Inner: i(2) = 2i

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​Last:

Multiple Choice

(2-i)(3+i)

• 5-i

• 7

• 7-i

Multiple Choice

Simplify the following radical: √32

• 3√2
• 4√8
• 16√2
• 4√2

Multiple Choice

Simplify the expression

$$\left(-6-5i\right)\left(1+3i\right)$$  

• $$10-23i$$  

• $$9-13i$$  

• $$-21-23i$$  

• $$9-23i$$  

Multiple Choice

(4+i)(5+i)

• 20+i

• 19+9i

• 9i

Multiple Choice

Simplify √-23

• -√23
• 23i
• 23
• i√23

​Complex Conjugates

​Dividing Complex Numbers

Multiple Choice

Simplify.

$$\left(3-2i\right)\div\left(-2-2i\right)$$  

• $$\frac{7+4i}{5}$$  

• $$\frac{-3+2i}{5}$$  

• $$\frac{-1+5i}{4}$$  

• $$\frac{3i+2}{2}$$  

Multiple Choice

Simplify.

$$\left(-1-3i\right)\div\left(-i\right)$$  

• $$-i+3$$  

• $$-1-3i$$  

• $$\frac{-4-3i}{2}$$  

• $$-9i$$  

​Graphing A Complex Number

​We graph or plot complex numbers on the complex number plane.

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​The x-axis is now the real axis and the y-axis is the imaginary axis.

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​A complex number is a point on the graph.