wiz-icon
MyQuestionIcon
MyQuestionIcon
5
You visited us 5 times! Enjoying our articles? Unlock Full Access!
Question

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


A

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C


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.


flag
Suggest Corrections
thumbs-up
23
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Solving Complex Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon