Complex Numbers Lesson 5 6 Algebra 2 Additional

Complex Numbers Lesson 5 -6 Algebra 2 Additional Examples Simplify – 54 = = – 1 • 54 – 1 • =i • 54 =i • 3 = 3 i 6 6 54 – 54 by using the imaginary number i.

Complex Numbers Lesson 5 -6 Algebra 2 Additional Examples Write – 121 – 7 in a + bi form. – 121 – 7 = 11 i – 7 = – 7 + 11 i Simplify the radical expression. Write in the form a + bi.

Complex Numbers Lesson 5 -6 Algebra 2 Additional Examples Find each absolute value. a. |– 7 i| – 7 i is seven units from the origin on the imaginary axis. So |– 7 i| = 7 b. |10 + 24 i| = = 102 + 242 100 + 576 = 26

Complex Numbers Lesson 5 -6 Algebra 2 Additional Examples Find the additive inverse of – 7 – 9 i –(– 7 – 9 i) Find the opposite. 7 + 9 i Simplify.

Complex Numbers Lesson 5 -6 Algebra 2 Additional Examples Simplify the expression (3 + 6 i) – (4 – 8 i) = 3 + (– 4) + 6 i + 8 i = – 1 + 14 i Use commutative and associative properties. Simplify.

Complex Numbers Lesson 5 -6 Algebra 2 Additional Examples Find each product. a. (3 i)(8 i) = 24 i 2 Multiply the real numbers. = 24(– 1) Substitute – 1 for i 2. = – 24 Multiply. b. (3 – 7 i )(2 – 4 i ) = 6 – 14 i – 12 i + 28 i 2 = 6 – 26 i + 28(– 1) = – 22 – 26 i Multiply the binomials. Substitute – 1 for i 2. Simplify.

Complex Numbers Lesson 5 -6 Algebra 2 Additional Examples Solve 9 x 2 + 54 = 0 9 x 2 = – 54 Isolate x 2 = – 6 x = ±i 6 Find the square root of each side. Check: 9 x 2 + 54 = 0 9(i 6)2 + 54 0 9(6)i 2 + 54 0 54(– 1) – 54 54 = 54 9 x 2 + 54 = 0 9(i(– 6))2 + 54 0 9(6 i 2) + 54 0 54(– 1) – 54 = – 54

Complex Numbers Lesson 5 -6 Additional Examples Algebra 2 Find the first three output values for f(z) = z 2 – 4 i. Use z = 0 as the first input value. f(0) = 02 – 4 i = – 4 i f(– 4 i )= (– 4 i )2 – 4 i First output becomes second input. Evaluate for z = – 4 i. = – 16 – 4 i f(– 16 – 4 i )= (– 16 – 4 i )2 – 4 i Second output becomes third input. Evaluate for z = – 16 – 4 i. = [(– 16)2 + (– 16)(– 4 i ) + (– 16)(– 4 i) + (– 4 i )2] – 4 i = (256 + 128 i – 16) – 4 i = 240 + 124 i The first three output values are – 4 i, – 16 – 4 i, 240 + 124 i.