Find all complex numbers satisfying |z+3+4i|=|z-5|

quiquenobi2v6

quiquenobi2v6

Answered question

2022-01-16

Find all complex numbers satisfying
|z+3+4i|=|z5|

Answer & Explanation

Jacob Homer

Jacob Homer

Beginner2022-01-17Added 41 answers

Step 1
|z+3+4i|=|z5|
Let z=z+iy
So |(x+3)+i(y+4)|=|(x5)+iy|
(x+3)2+(y+4)2=(x5)2+y2
x2+9+6x+y2+16+8y=x2+2510x+y2
16x+8y=0
wx+y=0
y=2x
So z=x2i
z=x(12i)
Ex x=1z=12i
x=2z=24i
z=3z=36i

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