HOW TO FIND EQUATION OF LOCUS OF COMPLEX NUMBERS

Question :

Obtain the Cartesian equation for the locus of z = x + iy in each of the following cases:

(i) |z − 4| = 16

Solution :

z = x + iy

|(x + iy) − 4| = 16

|(x  - 4) + iy| = 16

√(x - 4)2 + y2  =  16

Taking squares on both sides, we get

(x - 4)2 + y2  =  256

x2 - 2x(4) + 42 + y2  =  256

x2 + y2 - 8x + 16 - 256  =  0

x2 + y2 - 8x - 240  =  0

(ii) |z − 4|2 - |z - 1|2 = 16

Solution :

z = x + iy

|z − 4|2 - |z - 1|2 = 16

|(x + iy) − 4|2 - |(x + iy) - 1|2 = 16

|(x - 4) + iy|2 - |(x - 1) + iy|2 = 16

(√(x - 4)2 + y2)2 - (√(x - 1)2 + y2)2  =  16

(x - 4)2 + y2 - [(x - 1)2 + y2]  =  16

x2 - 8x + 16 + y2[x2 - 2x + 1 + y2]  =  16

x2 - 8x + 16 + y2 - x2 + 2x - 1 - y2  =  16

-6x + 15 - 16  =  0

-6x - 1  =  0

Multiply through out the equation by negative, we get

6x + 1  =  0

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. SAT Math Resources (Videos, Concepts, Worksheets and More)

    Dec 10, 24 05:46 AM

    SAT Math Resources (Videos, Concepts, Worksheets and More)

    Read More

  2. Digital SAT Math Problems and Solutions (Part - 85)

    Dec 10, 24 05:44 AM

    digitalsatmath72.png
    Digital SAT Math Problems and Solutions (Part - 85)

    Read More

  3. How to Find Slant Asymptote of a Function

    Dec 08, 24 08:11 PM

    slantasymptote.png
    How to Find Slant Asymptote of a Function (Oblique) - Examples with step by step explanation

    Read More