Prove each of the following statements. Fully state and explain each claim and logical step in...
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Prove each of the following statements. Fully state and explain each claim and logical step in your proof, using complete English sentences throughout. 1. Prove that if z is a complex number solution of a quadratic equation with real num- bers as coefficients, then z is also a complex number solution of the same quadratic equation. That is, if a, b, c are real numbers and z is a complex number such that az + bz+c=0, then a(z) 2 + b + c = 0. 2. Noting that (z + i)5 = z5 + 5iz 25+5iz4-1023 10z310iz + 5z + i prove that the five solutions of the equation 25+5iz41023 - 10iz + 5z = 0 are equally spaced around a circle of radius 1, but not centred at the origin. Prove each of the following statements. Fully state and explain each claim and logical step in your proof, using complete English sentences throughout. 1. Prove that if z is a complex number solution of a quadratic equation with real num- bers as coefficients, then z is also a complex number solution of the same quadratic equation. That is, if a, b, c are real numbers and z is a complex number such that az + bz+c=0, then a(z) 2 + b + c = 0. 2. Noting that (z + i)5 = z5 + 5iz 25+5iz4-1023 10z310iz + 5z + i prove that the five solutions of the equation 25+5iz41023 - 10iz + 5z = 0 are equally spaced around a circle of radius 1, but not centred at the origin.
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Related Book For
Macroeconomics
ISBN: 978-1464168505
5th Canadian Edition
Authors: N. Gregory Mankiw, William M. Scarth
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