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

quiquenobi2v6 2022-01-16 Answered
Find all complex numbers satisfying
|z+3+4i|=|z5|
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Expert Answer

Jacob Homer
Answered 2022-01-17 Author has 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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