Mathematical Problem Solving: Complex Numbers, Quadratic Equations, And Trigonometric Applications

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Mathematical Problem Solving: Complex Numbers, Quadratic Equations, and Trigonometric Applications 1. Solve for the value of −−144 - \ sqrt{ - 144} −−144 , and express the result in terms of the imaginary unit ii i . Would that work as a question for your answer? − √ − 144 = − √ 144 . ( − 1 ) = − 12 √ ( − 1 ) = − 12 𝑖 2. Solve the quadratic equation 6y2=43y6y^2 = 43y 6y2 = 43y . 6 𝑦 2 = 43 𝑦 6 𝑦 2 − 43 𝑦 = 0 𝑦 ( 6 𝑦 − 43 ) = 0 𝑠𝑜 𝑒𝑖𝑡 ℎ 𝑒𝑟 𝑦 = 0 𝑜𝑟 6 𝑦 − 43 = 0 6 𝑦 = 43 𝑦 = 43 6 𝑠𝑜 𝑡 ℎ 𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 𝑎𝑟𝑒 𝑦 = 0 𝑎𝑛𝑑 43 6 3. Solve the quadratic equation 3n2=−11n+203n^2 = - 11n + 20 3n2 = − 11n + 20 . 3 𝑛 2 = − 11 𝑛 + 20 3 𝑛 2 + 11 𝑛 − 20 = 0 3 𝑛 2 + 15 𝑛 − 4 𝑛 − 20 = 0 3 𝑛 ( 𝑛 + 5 ) − 4 ( 𝑛 + 5 ) = 0 ( 3 𝑛 − 4 ) ( 𝑛 + 5 ) = 0 𝑠𝑜 3 𝑛 − 4 = 0 𝑜𝑟 𝑛 + 5 = 0 𝑛 = 4 3 , − 5 4. Find the product of − 3i - 3i − 3i and 4i4i 4i . − 3 𝑖 . 4 𝑖 = − 12 𝑖 2 𝑤𝑒 𝑘𝑛𝑜𝑤 𝑖 = √ − 1 𝑠𝑜 𝑖 2 = − 1 − 12 𝑖 2 = − 12 ( − 1 ) = 12
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