Given that Z1 and Z2 are complex numbers, show geometrically or otherwise that |Z1| - |Z2| is less than or equal to |Z1 - Z2|. Hence or otherwise, show that if Z is a number such that |Z2 - 3Z|=|4eix| where x is real, then |Z| is less than or equal to 4.

Given that Z1 and Z2 are complex numbers, show geometrically or otherwise that |Z1| - |Z2| is less than or equal to |Z1 - Z2|. Hence or otherwise, show that if Z is a number such that |Z2 - 3Z|=|4eix| where x is real, then |Z| is less than or equal to 4.

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

Given that Z₁and Z₂are complex numbers, show geometrically or otherwise that |Z₁| - |Z₂| is less than or equal to |Z_{1 -}Z₂|.

Hence or otherwise, show that if Z is a number such that |Z² - 3Z|=|4e^ix| where x is real, then |Z| is less than or equal to 4.

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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