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The number of complex numbers z such that |z+1|=|z-3| equals :

Question

The number of complex numbers $z$ such that $∣ z + 1∣ = ∣ z - 3∣$ equals :-

0

1

2

\infty

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The number of complex numbers

z

such that

∣ z + 1∣ = ∣ z - 3∣

equals :-

7 mins ago

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7 mins ago

Text solutionVerified

For

z = x + i y

with

x, y

are real numbers.

Given,

∣ z - 1∣ = ∣ z + 1∣

or,

(x + 1)^{2} + y^{2} = (x - 3)^{2} + y^{2}

or,

(x + 1)^{2} + y^{2} = (x - 3)^{2} + y^{2}

or,

(x + 1)^{2} = (x - 3)^{2}

or,

x + 1 = - (x - 3)

[ Taking the negative sign other we will get some contradiction]

or,

2 x = 2

or,

x = 1

\forall y \in R

So it is true for infinitely many value of

y

So we've infinitely many

z

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Question Text	The number of complex numbers $z$ such that $∣ z + 1∣ = ∣ z - 3∣$ equals :-
Answer Type	Text solution:1
Upvotes	150