Find all complex numbers satisfying

$|z+3+4i|=|z-5|$

quiquenobi2v6
2022-01-16
Answered

Find all complex numbers satisfying

$|z+3+4i|=|z-5|$

You can still ask an expert for help

Jacob Homer

Answered 2022-01-17
Author has **41** answers

Step 1

$|z+3+4i|=|z-5|$

Let$z=z+iy$

So$|(x+3)+i(y+4)|=|(x-5)+iy|$

$\sqrt{{(x+3)}^{2}+{(y+4)}^{2}}=\sqrt{{(x-5)}^{2}+{y}^{2}}$

$x}^{2}+9+6x+{y}^{2}+16+8y={x}^{2}+25-10x+{y}^{2$

$16x+8y=0$

$wx+y=0$

$y=-2x$

So$z=x-2i$

$z=x(1-2i)$

Ex$x=1\Rightarrow z=1-2i$

$x=2\Rightarrow z=2-4i$

$z=3\Rightarrow z=3-6i$

Let

So

So

Ex

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