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Simplify and Find Zeros: Complex Numbers Mathematics Guide

Explore how to simplify complex equations using FOIL, isolating terms, and finding zeros for more efficient math calculations. Learn to rewrite functions in linear factored form and work with rational and complex zeros step by step.

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Simplify and Find Zeros: Complex Numbers Mathematics Guide

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  1. Alternative, less work! Combine both complex zeros with + sign. The author wants you to FOIL! Isolate the i term. Square both sides. STOP! TOO MUCH WORK!

  2. Multiply

  3. Find the zeros of . Rewrite f(x) in linear factored form. Zeros at x = -2 The next zero is a fraction between 0 and 1. The rational zero test gives us 1/3 or 2/3. Try 1/3. x = 1/3 We have two rational zeros and time to factor them out to a quadratic function.

  4. Find the zeros of . Rewrite f(x) in linear factored form. 3 5 25 45 -18 Zeros at x = -2 x = 1/3 x = + 3i -6 2 -54 18 -2 3 -1 27 -9 0 Factored form. ( x + 2 ) ( 3x – 1 ) ( x + 3i ) ( x – 3i ) 1 0 9 3 0 27 0 1/3 Solve for x.

  5. Find the zeros of . Given one of the zeros is x = 3 + 2i 1 -10 36 -46 -13 3 + 2i -25 – 8i 49 – 2i 13 3 + 2i 1 -7 + 2i 11 – 8i 3 – 2i 0 3 – 2i -12 + 8i -3 + 2i Go to MODE and turn on a + bi 3 – 2i 1 - 4 -1 0 Complete the square. These are the exact values!

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