GATE IN 2022 | Question: 40

Question

For the complex number $z= \frac{a+jb}{a-jb},$ where $a>0$ and $b>0.$

Which of the following statement(s) is/are true?

• A. The phase is $2 \; \tan^{-1}\frac{b}{a}$
• B. The phase is $ \; \tan^{-1}\frac{2b}{a}$
• C. The magnitude is $1$
• D. The magnitude is $\sqrt{\frac{a^{2}+b^{2}}{a^{2}-b^{2}}}$