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Question

Find the complex number z satisfying the equations z12z8i=53,  z4z8=1



Your Answer
A

6

Your Answer
B

Correct Answer
C

Your Answer
D

None of these


Solution

The correct option is B


We have z12z8i=53,  z4z8=1

Let z=x+iy, then

z12z8i=53 3|z-12| = 5|z-8i|

3|(x-12) + iy| = 5|x + (y-8)i|

9(x12)2+9y2 = 25x2+25(y8)2     (i)

z4z8=1 |z-4| = |z-8|

(x-4 + iy| = |x -8+iy|

(x4)2+y2 = y2+(x8)2  x=6

Putting x=6 in (i), we get y2-25y+136=0

 y=17, 8

Hence z=6+17i or z=6+8i

Trick: Check it with options.

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