If $|z|=1$ and $z \neq 0,$ then the points $z+\frac{1}{z}$ lie on a

Straight line not through the origin

Line segment lying on the y-axis

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Medium

1 of 1

Application +4 | -1

|z|=1

and

z \neq 0,

then the points

z+\frac{1}{z}

lie on a

View answer and explanation

Correct option: C

Line segment lying on the x-axis

Option C is correct. Since |z|=1, z can be represented as e^(iθ). Therefore, z + 1/z = 2cos(θ), which is a real number between -2 and 2, representing a line segment on the x-axis.

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