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  • Let represents the principal argument of the complex number <img alt="\mathrm{z}" src="

Let \mathrm{arg(z)} represents the principal argument of the complex number \mathrm{z}. Then \mathrm{|z|=3} and  \mathrm{\arg (z-1)-\arg (z+1)=\frac{\pi}{4}} intersects

Option: 1

exactly at one point


Option: 2

exactly at two point


Option: 3

nowhere


Option: 4

at infinitely many points


Answers (1)

best_answer

\mathrm{\arg (z-1)-\arg (z+1)=\frac{\pi}{4}} \\

\mathrm{\Rightarrow \operatorname{arg}\left(\frac{z-1}{z+1}\right)=\frac{\pi}{4}}

\Rightarrow Major arc of a circle sutending \frac{\pi}{4} at circumference.

So, they do not intersect.

Hence the correct answer is option 3

Posted by

Kuldeep Maurya

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