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Complex Numbers: Standard Form, Add, Subtract, Multiply, Divide, Quadratic Formula, and Powers of "i

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This guide explains complex numbers in standard form, demonstrates how to add, subtract, multiply, and divide complex numbers, solves quadratic equations using the quadratic formula, and evaluates powers of "i".

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Complex Numbers: Standard Form, Add, Subtract, Multiply, Divide, Quadratic Formula, and Powers of "i

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  1. 2.4 Complex Numbers Standard form of a complex number a + bi Adding and Subtracting complex numbers (3 – i) + (2 + 3i) = 2i + (-4 – 2i) = 3 - (-2 + 3i) + (-5 + i) = 5 + 2i -4 -2i

  2. Multiplying Complex numbers Note: i2 = -1 (i)(-3i) = (2 – i)(4 + 3i) = (3 + 2i)(3 – 2i) = -3i2 = 3 8 + 6i – 4i – 3i2 = 11 + 2i 9 – 4i2 = 9 + 4 = 13 -6 Dividing Complex numbers

  3. Note: -6 -3

  4. Use the quadratic formula to solve 0 = 3x2 – 2x + 5

  5. i1 = i i2 = -1 i3 = -i i4 = (i2)2 = (-1)2 = 1 i5 = i What does i36 = (i2)18 = (-1)18 = 1 i53 = i

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