A2M1L37SB Imaginary Numbers Part 1.notebook Imaginary Numbers Standards: NCN.A.1 NCN.A.2 November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook Solve each equation for x: 1) x1 = 0 2) x + 1 = 0 3) x2 1= 0 4) x2 + 1= 0 November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook November 10, 2015 Imaginary Numbers the imaginary unit represents √ -1 i Practice using the imaginary unit by simplifying the following: i = √-1 A2M1L37SB Imaginary Numbers Part 1.notebook Counting Numbers 1,2,3... November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook Whole Numbers 0,1,2,3... Counting Numbers 1,2,3... November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook Integers ...-3,-2,-1,0,1,2,3... Whole Numbers 0,1,2,3... Counting Numbers 1,2,3... November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook Rational Numbers (integers plus fractions) Integers ...-3,-2,-1,0,1,2,3... Whole Numbers 0,1,2,3... Counting Numbers 1,2,3... November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook Rational Numbers (integers plus fractions) Integers ...-3,-2,-1,0,1,2,3... Irrational Numbers (non-repeating, Whole non-terminal Numbers decimals) 0,1,2,3... Counting Numbers 1,2,3... November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook Real Numbers Rational Numbers (integers plus fractions) Integers ...-3,-2,-1,0,1,2,3... Irrational Numbers (non-repeating, Whole non-terminal Numbers decimals) 0,1,2,3... Counting Numbers 1,2,3... November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook November 10, 2015 Real Numbers Rational Numbers (integers plus fractions) Integers ...-3,-2,-1,0,1,2,3... Irrational Imaginary Numbers Numbers (non-repeating, Whole non-terminal Numbers decimals) 0,1,2,3... Counting Numbers 1,2,3... √-1 A2M1L37SB Imaginary Numbers Part 1.notebook Complex Numbers (real + Imaginary) Real Numbers Rational Numbers (integers plus fractions) Integers ...-3,-2,-1,0,1,2,3... Irrational Numbers (non-repeating, Whole non-terminal Numbers decimals) 0,1,2,3... Counting Numbers 1,2,3... November 10, 2015 Examples of Complex numbers 23i, 5+ 8i, 7+2i, 16 9i Imaginary Numbers √-1 3i, 5i, -2i A2M1L37SB Imaginary Numbers Part 1.notebook Complex numbers 6+3i 4 + 0i 0 + 3i 2 + 5i November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook November 10, 2015 Solve using the quadratic formula 1. x2 + 9 = 0 2. x2 + 4x + 8 = 0 A2M1L37SB Imaginary Numbers Part 1.notebook Plot i 1) 4i i 2)3i i 3) 4+5i i 4) 23i i 5) 1+4i i i i i November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook R90 November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook November 10, 2015 Powers of i 0 i = i1 = 2 i = i3 = i4 = 5 i = 6 i = i7 = i8 = i9 = i10 = i11 = i12 = 13 i = i14 = 15 i = A2M1L37SB Imaginary Numbers Part 1.notebook November 10, 2015 Procedure for Simplifying Powers of i Example: Simplify i35 1) Divide the exponent by 4. 2) Use the remainder as the new exponent. 3) Write in a + bi form i35 = i 8 R3 4 35 32 3 i3 0 + i or i A2M1L37SB Imaginary Numbers Part 1.notebook November 10, 2015 Division by 4 and the possible remainders Remainder of 0 = .0 Remainder of 1 = .25 Remainder of 2 = .5 Remainder of 3 = .75 A2M1L37SB Imaginary Numbers Part 1.notebook November 10, 2015 Write in a + bi form: 40 1) i 2) i53 3) i18 4) i2003 A2M1L37SB Imaginary Numbers Part 1.notebook Review: November 10, 2015 A2M1L37SB Imaginary Numbers Part 1.notebook Homework Worksheet November 10, 2015
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