Operations on 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

Subtracting Complex Numbers

• (4-5i)-(1-8i)

• =(4-5i)+(-1+8i) (Distribute negative)

• =3+3i (Combine like terms)

Multiple Choice

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

• 34i

• 28+6i

• 12+5i

• -4+9i

Multiple Choice

(3-2i)-(4-2i)=

• -1+0i

• 7-4i

• 1-2i

• -i

Multiple Choice

(5+8i)+(6-10i)

• -1-18i

• 11-2i

• 13-4i

• -20i

Multiple Choice

(-9-5i)-(2-7i)

• -40+14i

• -7-12i

• -59i

• -11+2i

Multiplying Complex Numbers

• Remember to FOIL or use the box method

• i²=-1 so this means replace any i² with a -1

• Simplify as much as possible.

Multiplying Complex Numbers

(8+2i)(7-3i)

=56-24i+14i-6i²

=56-10i-6(-1)

=56-10i+6

=62-10i

Multiple Choice

(2-i)(3+i)

• 5-i

• 7

• 7-i

Multiple Choice

(4+i)(5+i)

• 20+i

• 19+9i

• 9i

Multiple Choice

(3-4i)(2+i)

• -12+2i

• -24i

• 10-5i

Multiple Choice

(5-3i)(2-5i)

• 25-31i

• -5-31i

• -15-10i

• -25i