JEE Mains · Maths · STD 11 - 4.1 complex nubers
If the complex number \(z=2-i\left(2 \tan \frac{5 \pi}{8}\right)\) has modulus \(r\) and argument \(\theta\), then what are \((r, \theta)\) ?
- A \(\left(2 \sec \frac{3 \pi}{8}, \frac{3 \pi}{8}\right)\)
- B \(\left(2 \sec \frac{3 \pi}{8}, \frac{5 \pi}{8}\right)\)
- C \(\left(2 \sec \frac{5 \pi}{8}, \frac{3 \pi}{8}\right)\)
- D \(\left(2 \sec \frac{11 \pi}{8}, \frac{11 \pi}{8}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(2 \sec \frac{3 \pi}{8}, \frac{3 \pi}{8}\right)\)
Step-by-step Solution
Detailed explanation
\( z=2-i\left(2 \tan \frac{5 \pi}{8}\right)=x+i y(\text { let }) \) \( r=\sqrt{x^2+y^2} \theta=\tan ^{-1} \frac{y}{x} \) \( r=\sqrt{(2)^2+\left(2 \tan \frac{5 \pi}{8}\right)^2} \) \( =\left|2 \sec \frac{5 \pi}{8}\right|=\left|2 \sec \left(\pi-\frac{3 \pi}{8}\right)\right|\)…
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