Writing Imaginary and Complex Numbers

Complex Numbers (Operations)

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Complex Number

A complex number has the form a +bi, where a is the real component and b is the imaginary component.

Ex.

6-3i

0+5i

8+0i

-3+7i

Operations with Complex Numbers

Operations with complex numbers are similar to expressions with variables. You can combine real components with each other and imaginary components with each other.

When multiplying imaginary components, you add exponents, similar to multiplying variables.

Adding/Subtracting Complex Numbers

• Combine real terms

• Combine imaginary components

• Distribute negative first (when subtracting)

Adding Complex Numbers

(2+3i)+(8-4i)

=10+-i (Add 2+8 and 3i+-4i)

=10-i

Multiple Choice

(4+7i)+(8-2i)=

• 34i

• 28+6i

• 12+5i

• -4+9i

Multiple Choice

(4+i)(5+i)

• 20+i

• 19+9i

• 9i

Complex Numbers

Real + Imaginary Number

a + bi

example: 2 + 3i

What is an imaginary number?

Multiple Choice

$$\sqrt{-48}$$  

• $$4i\sqrt{3}$$  

• $$3i\sqrt{12}$$  

• $$-4\sqrt{3}$$  

• $$-8\sqrt{6}$$  

Multiple Choice

$$\sqrt{-80}$$  

• $$2i\sqrt{20}$$  

• $$4i\sqrt{5}$$  

• $$-8\sqrt{10}$$  

Multiple Choice

$$3\sqrt{-90}$$  

• $$3i\sqrt{10}$$  

• $$9i\sqrt{10}$$  

• $$27i\sqrt{10}$$