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Class 11
>>Applied Mathematics
>>Number theory
>>Complex Numbers
>>The complex number z satisfying the equa
Question

The complex number z satisfying the equations ∣z∣−4=∣z−i∣−∣z+5i∣=0, is
This question has multiple correct options
A
3−i
B
23−2i
C
−23−2i
D
0
Medium
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Updated on : 2022-09-05
Solution

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Correct options are B) and C)
We have two equation ∣z∣−4=0 and ∣z−i∣−∣z+5i∣=0
Putting z=x+iy i.e x2+y2=16 ....(1)
and ∣x+iy−i∣=∣x+iy+5i∣
⇒x2+(y−1)2=x2+(y+5)2
⇒y=−2 ...(2)
Putting y=−2 in (1),
x2+4=16⇒x=±2
Explanation:
Hence the complex numbers z satisfying the given equation are
z1=23−2i and z2=−23−2i