O Let a, b, and c be any three nonzero complex numbers. If|z| = 1 and 'z' satisfies the equation az + bz + c = 0, prove thataā=i=ce and la b= √√ac (b)²

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Answered: Let a, b, and c be any three nonzero…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.5: Trigonometric Form For Complex Numbers

Problem 38E

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Similar questions

Prove that for complex numbers .
Determine the number and nature of the roots of the equation in Exercise 67. Calculate the discriminant associated with the equation 6x2+5x+1=0.
Recall from the introduction to Section 8.2 that Jerome Cardans solutions to the equation x3=15x+4 could be written as x=2+11i3+211i3 Lets assume that the two cube roots are complex conjugates. If they are, then we can simplify our work by noticing that x=2+11i3+211i3=a+bi+abi=2a which means that we simply double the real part of each cube root of 2+11i to find the solutions to x3=15x+4. Now, to end our work with Cardan, find the three cube roots of 2+11i. Then, noting the discussion above, use the three cube roots to solve the equation x3=15x+4. Write your answers accurate to the nearest thousandth.

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Let a, b, and c be any three nonzero complex numbers. If |z| = 1 and 'z' satisfies the equation az + bz + c = 0, prove that aa = cc and la| |b|= √√ac (5)².