COMEDK · Maths · 3. Complex Number
What is the argument of the complex number \(\dfrac{(1+i)(2+i)}{3-i}\), where \(i=\sqrt{-1}\) ?
- A 0
- B \(\dfrac{\pi}{4}\)
- C \(-\dfrac{\pi}{4}\)
- D \(\dfrac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
Let \(z = \dfrac{(1+i)(2+i)}{3-i}\). First, simplify the numerator: \((1+i)(2+i) = 2 + i + 2i + i^{2} = 2 + 3i - 1 = 1 + 3i\). Now, multiply the numerator and denominator by the conjugate of the denominator \((3+i)\):…
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