Answer to Question #228679 in Algebra for Cheryl-Ann

Question #228679

the locus of the complex number z such that Iz+3I = Iz-1I is?

A.     A line

B.     A circle

C.     A quadratic curve

An ellipse 


1
Expert's answer
2021-09-14T06:05:07-0400

Given that "|z+3|=|z-1|"

Let "z=x+iy"

"|x+iy+3|=|x+iy-1|\\\\\n\\Rightarrow \\sqrt{(x+3)^2+y^2}=\\sqrt{(x-1)^2+y^2}\\\\"

Squaring both sides, we get:

"(x+3)^2+y^2=(x-1)^2+y^2\\\\\n\\Rightarrow x^2+9+6x=x^2+1-2x\\\\\n\\Rightarrow 8x+8=0\\\\\n\\Rightarrow x=-1"

Therefore, the locus of a given complex number is a line.

Hence, the correct option is (A).


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS