# Complex Numbers

Equations

VOCABULARY & Properties

• Imaginary unit -- the number i
Note
: This is used to take the square root of
negative
numbers.
Complex Numbers -- numbers of the form
a + bi (a is “ real ”, b is “imaginary”)
• Example: 2 + 3i or 4 - 7i

Know the perfect squares : 1, 4, 9, 16, 25, 36, 49, 64, 81,
100, 121, 144, 169, 196, 225,…,400, 625, 900, 1000,…

See Example 1, page 535

Because and are easily confused,
we usually write

Multiplication

When multiplying radicals with negatives , take
the root first, then multiply. Otherwise, you’ll

taking root first vs. multiplying first

See Examples 2 & 3, page 540.

See Example 4, page 537.
To add or subtract , combine like terms .

• i) (3 + 5i ) + (2 - 4i )
• j) (4 - 6i ) - (3 - 7i )
• k) (9+i ) – (3 + 2i ) + (-5 – 3i )

For binomials , use the distributive property or
FOIL
. (Don’t forget to substitute -1 for i^2.)

Complex Conjugates

• When dividing, we cannot leave a complex
number in the denominator.

• If the denominator is a binomial , multiply by its
conjugate to rationalize the denominator.

PRACTICE
Find the conjugate & multiply.

Divide.

Summary

• Complex numbers standard form: a+bi
• To add or subtract, combine like terms .
• Simplify before multiplying.
• Always substitute -1 for i^2.
• Never leave an imaginary unit in the
denominator.

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