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Question

If z-25z-1=5, then find the value of z


A

3

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B

4

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C

5

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D

6

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Solution

The correct option is C

5


Explanation for the correct option.

Step 1. Simplify the given equation.

Let z=x+iy, then the equation z-25z-1=5 becomes:

z-25z-1=5x+iy-25x+iy-1=5ab=abx-25+iy=5x-1+iyx-252+y2=5x-12+y2

Now, square both sides and simplify.

x-252+y22=5x-12+y22x2-50x+625+y2=25x2-2x+1+y2x2-50x+625+y2-25x2+50x-25-25y2=0-24x2+y2+600=0-24x2+y2=-600x2+y2=25

Step 2. Find the modulus of z.

For the complex number z=x+iy, the modulus is given as:

z=x2+y2=25x2+y2=25=5

Thus the value of z is 5.

Hence, the correct option is C.


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