This is a question from a competitive entrance exam ....I just want to check whether my approach is correct as i dont have the answer keys .(adsbygoogle = window.adsbygoogle || []).push({});

here is the question :

How many complex numbers z are there such that |z+ 1| = |z+i| and |z| = 5?

(A) 0

(B) 1

(C) 2

(D) 3

My approach :

let z = x+iy

Now, using |z+ 1| = |z+i|,

|(x+1)+iy| = |x+(y+1)i|

Simplifying this, i got x=y......(1)

and since |z| = 5 , we have √(x^{2}+y^{2}) = 5

which means (x^{2}+y^{2}) = 25 ......(2)

Now, plugging (1) in (2) , we get

x^{2}= (25/2)

therefore x can take 2 values similarly y also can take 2 values.....

and since x=y in the complex number .....we have 2 solutions and hence the answer is 2

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# B Complex number solutions

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