COMEDK · Maths · 3. Complex Number
The complex number \(\dfrac{1+7 i}{(2-i)^2}\) lies in
- A Quadrant 1
- B Quadrant 2
- C Quadrant 4
- D Quadrant 3
Answer & Solution
Correct Answer
(B) Quadrant 2
Step-by-step Solution
Detailed explanation
Given the complex number \(z = \dfrac{1+7i}{(2-i)^2}\). First, expand the denominator: \((2-i)^2 = 4 - 4i + i^2 = 4 - 4i - 1 = 3 - 4i\). Now, express \(z\) as \(\dfrac{1+7i}{3-4i}\). Multiply the numerator and denominator by the conjugate of the denominator, which is \(3+4i\):…
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