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Question

If z is a complex number such that z=-z, then


A

z is purely real

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B

z is purely imaginary

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C

z is any complex number

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D

real part of z is same as its imaginary part

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Solution

The correct option is B

z is purely imaginary


Explanation for the correct option.

Find the real and imaginary part of z.

Let z=x+iy be a complex number.

Now the conjugate of z is given as: z=x-iy.

It is given that z=-z so substitute the values in the equation and simplify.

z=-zx+iy=-(x-iy)x+iy=-x+iyx+iy+x-iy=02x=0x=0

So the real part of the complex number z is 0.

So, the complex number z is purely imaginary that is z=iy.

Hence, the correct option is B.


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