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

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Mathematical Problem Solving: Complex Numbers, Quadratic Equations,and Trigonometric Applications1.Solve for the value of−−144-\sqrt{-144}−−144, and express the result in terms of theimaginary unitiii.Would that work as a question for your answer?−√−144=−√144.(−1)=−12√(−1)=−12𝑖2.Solve the quadratic equation6y2=43y6y^2 = 43y6y2=43y.6𝑦2=43𝑦6𝑦2−43𝑦=0𝑦(6𝑦−43)=0𝑠𝑜𝑒𝑖𝑡ℎ𝑒𝑟𝑦=0𝑜𝑟6𝑦−43=06𝑦=43𝑦=436𝑠𝑜𝑡ℎ𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠𝑎𝑟𝑒𝑦=0𝑎𝑛𝑑4363.Solve the quadratic equation3n2=−11n+203n^2 =-11n + 203n2=−11n+20.3𝑛2=−11𝑛+203𝑛2+11𝑛−20=03𝑛2+15𝑛−4𝑛−20=03𝑛(𝑛+5)−4(𝑛+5)=0(3𝑛−4)(𝑛+5)=0𝑠𝑜3𝑛−4=0𝑜𝑟𝑛+5=0𝑛=43,−54.Find the product of−3i-3i−3iand4i4i4i.−3𝑖.4𝑖=−12𝑖2𝑤𝑒𝑘𝑛𝑜𝑤𝑖=√−1𝑠𝑜𝑖2=−1−12𝑖2=−12(−1)=12

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