Any questions about the practice? Page , 11, 13, 21, 25, 27, 39, 41, 53

A.2, –1 B.1, 2 C.1, 1 D.–1, 1 1. Solve x 2 – x = 2 by factoring. A.1, 4 B.0, 16 C.–1, 4 D.–16 3. Solve z 2 = 16z by factoring. A.2 B.4 C.8 D Solve c 2 – 16c + 64 = 0 by factoring.

A.2, –1 B.1, 2 C.1, 1 D.–1, 1 1. Solve x 2 – x = 2 by factoring. A.1, 4 B.0, 16 C.–1, 4 D.–16 3. Solve z 2 = 16z by factoring. A.2 B.4 C.8 D Solve c 2 – 16c + 64 = 0 by factoring.

5.4 Complex numbers Goals: Simplify complex radicals Combine Complex Numbers

Square Roots of Negative Numbers Answer: A.

Square Roots of Negative Numbers B. Answer:

What is i ? i = √ -1 i 2 = -1 i 3 = - √ -1 = -i i 4 = 1 Ex: √ -16 √ -9 √ -28 √ -32y 3 √ - 80x 2 y 4

A. B. C. D. A.

Products of Pure Imaginary Numbers A. Simplify –3i ● 2i. –3i ● 2i=–6i 2 =–6(–1)i 2 = –1 = 6 B.

To multiply Multiply i’s first Multiply numbers Simplify -3i · 2i-12 · -2

A.15 B.–15 C.15i D.–8 A. Simplify 3i ● 5i.

Equation with Pure Imaginary Solutions Solve 5y = 0. 5y =0Original equation 5y 2 =–20Subtract 20 from each side. y 2 =–4Divide each side by 5. Take the square root of each side.

Simplifying/ solving equations To simplify……. Divide exponent of i by 4 and find out remainder. This will be your power of i. i 35 i 14 i 8 i 9 Solve equations like normal. You must simplify answer 5y = o

Finding Unknown Variables –Set real parts equal –solve –Set imaginary parts equal- solve 2x + yi = i

Adding/ Subtracting/ Multiplying –Solve as normal (treat i like a variable) –Evaluate any powers of I ( 3 + 5i) + (2 – 4i)( 3 + 5i) - (2 – 4i) ( 3 + 5i)(2 – 4i)

Divide Complex Numbers 3 – 2i and 3 + 2i are conjugates. Multiply. i 2 = –1 a + bi form Answer: A.

Dividing You cannot have i’s in the denominator!!! –Monomial? Multiply top and bottom by i – Binomial? Multiply top and bottom by conjugate 4 – i 5i 5i 3 + 2i

Practice Assignment Page 280, odd