JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

z

is any complex number satisfying

|z-1|=1

then which of the following is correct?

View answer and explanation

Correct option: A

\arg (z-1)=2 \arg (z)

Option A (

\arg (z-1)=2 \arg (z)

) is correct because, by letting

z-1=e^{i \theta}

, we can express

z

in terms of

\theta

and show that

\arg(z) = \frac{{\theta}}{{2}}

, which leads to

\arg(z-1) = 2 \arg(z)

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