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Question

The complex numbers z=x+iy which satisfy the equation z-5iz+5i=1 lie on which of the following.


A

The x - axis

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B

The straight line y=5

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C

a circle passing through the origin

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D

None of these

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Solution

The correct option is A

The x - axis


Explanation for correct answer :

Finding where z lies:

Given, z=x+iy is the satisfying the equation z-5iz+5i=1.

So, here we are substituting the value of z in equation.

x+iy-5ix+iy+5i=1x+i(y-5)x+i(y+5)=1x2+y-52x2+(y+5)2=1(x+iy=x2+y2)x2+y-52=x2+(y+5)2

Squaring both sides we get,

x2+y2+25-10y=x2+y2+25+10y20y=0y=0

Hence, z lies on x - axis.

Thus, the correct answer is Option (A).


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