Question
Find the complex number z satisfying the equations ∣∣z−12z−8i∣∣=53, ∣∣z−4z−8∣∣=1
Answer: Option C
:
C
We have ∣∣z−12z−8i∣∣=53, ∣∣z−4z−8∣∣=1
Let z=x+iy, then
∣∣z−12z−8i∣∣=53 ⇒ 3|z-12| = 5|z-8i|
⇒ 9(x−12)2+9y2 = 25x2+25(y−8)2 ⋯⋯(i)
∣∣z−4z−8∣∣=1 ⇒ |z-4| = |z-8|
⇒ (x−4)2+y2 = y2+(x−8)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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:
C
We have ∣∣z−12z−8i∣∣=53, ∣∣z−4z−8∣∣=1
Let z=x+iy, then
∣∣z−12z−8i∣∣=53 ⇒ 3|z-12| = 5|z-8i|
⇒ 9(x−12)2+9y2 = 25x2+25(y−8)2 ⋯⋯(i)
∣∣z−4z−8∣∣=1 ⇒ |z-4| = |z-8|
⇒ (x−4)2+y2 = y2+(x−8)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.
Was this answer helpful ?
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