P represents the variable complex number z = x + iy. Show that if z+1/z+i is purely imaginary, the locus of Pis a circle C and precise its center and radius. Show further that C goes through the origin and determine the equation of tangent to C at the origin

P represents the variable complex number z = x + iy. Show that if z+1/z+i is purely imaginary, the locus of Pis a circle C and precise its center and radius. Show further that C goes through the origin and determine the equation of tangent to C at the origin

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.4: Complex And Rational Zeros Of Polynomials

Problem 36E

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Question

P represents the variable complex number z = x + iy. Show that if z+1/z+i is purely imaginary, the locus of Pis a circle C and precise its center and radius.

Show further that C goes through the origin and determine the equation of tangent to C at the origin.

Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.

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