**Review of Solving Radical **

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

**Review of Simplifying Radicals **

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

get the wrong answer.

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.