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August 30, 2013 Algebra II Unit B: Radicals and Complex Numbers Section 4.6 Perform Operations with Complex Numbers Objectives *Add, subtract, multiply & divide complex numbers *Evaluate powers of i Assignment: Worksheet 4-6 August 30, 2013 Complex Numbers Standard form: a + bi or a - bi Ex: Ex: Adding and Subtracting Complex Numbers (a + bi) + (c + di) = (a+c) + (b+d)i a) (12 + 4i) + (3 + 2i) b) (-3 + i) + (2 - 2i) c) (-5 - i) + (-1 - i) d) (12 + 4i) - (3 + 2i) e) (-3 + i) - (2 - 2i) f) (-5 - i) - (-1 - i) August 30, 2013 Ex: Multiplying Complex Numbers Remember how to F.O.I.L. (x + 3)(x - 7) a) 2i(3 + 4i) b) -4(2 - 3i) c) -3i(6 + 2i) d) (3 + i)(5 + i) e) (4 + i)(2 - 3i) f) (-6 - 2i)(-3 - 4i) g) (2 + 2i) 2 h) (7 - 4i) 2 August 30, 2013 Use properties of exponents to simplify. Write complex numbers in standard form. a) 2 + 4i 4 7 b) -4 - 6i Now solve a quadratic equation with complex numbers. 2 a) 2x + 11 = -37 2 b) 2x + 18 = -72