If Z,=1+2i , find the Set of values of Zfor which1) f ZOf Zz%3D%3D

Name: If Z,=1+2i , find the Set of values of Zfor which1) f ZOf Zz%3D%3D
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Description: If Z,=1+2i , find the Set of values of Zfor which1) f ZOf Zz%3D%3D

Given z1 = 1+2i Let z2 = x+yi (i) We want |z1 + z2| = |z1| + |z2| We have: Thus According to the…

Answered: If Z,=1+2i , find the Set of values of…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter9: Real Numbers And Right Triangles

Section: Chapter Questions

Problem 8CST

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Question

If Z,=1+2i , find the Set of values of Z
for which
1) f Z
Of Zz
%3D
%3D

Expert Solution

Step 1

Given z₁ = 1+2i

Let z₂ = x+yi

(i) We want |z_{1 +}z₂| = |z₁| + |z₂|

We have:

Thus

According to the question; (a) = (b)

Squaring both sides

Again Squaring both sides:

Hence, z₂ = x+2xi = x(1+2i) = z₁x

Or z₂ is set of all values that lie on the line 2x = y

Step 2

(ii) We want |z₁ + z₂| = |z₁| - |z₂|

According to the question; (a) = (b)

Squaring both sides:

Again Squaring both sides:

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