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Question

If z+iz-i=3, then the radius of the circle is


A

221

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B

121

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C

3

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D

21

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Solution

The correct option is C

3


Find the radius of the circle.

Let z=x+iy.

Now, the equation z+iz-i=3 can be written as:

z+iz-i=3z+iz-i=3x+iy+i=3x+iy-iz=x+iyx+y+1i=3x+y-1ix2+y+12=3x2+y-12z=x+iy,z=x2+y2

Now square both sides and simplify.

x2+y+122=3x2+y-122x2+y2+1+2y=3x2+y2+1-2yx2+y2+1+2y-3x2-3y2-3+6y=0-2x2-2y2-2+8y=0-2x2+y2-4y+1=0x2+y2-4y+1=0

Now write the equation of circle in standrad form.

x2+y2-4y+1=0x2+y2-4y+4+1-4=0x2+y-22=3x2+y-22=32

On comparing the equation x2+y-22=32 with the standard equation of circle x-h2+y-k2=r2 it can be noticed that the center of the circle is 0,2 and its radius is 3.

So the radius of the circle is 3.

Hence, the correct option is C.


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