COMEDK · Maths · 3. Complex Number
Given that \(z\) is a real number and \(z=\dfrac{\lambda+4 i}{1+\lambda i}\) where \(\lambda \in R\), then the possible value of \(\lambda\) is
- A \(-2\)
- B \(2 i\)
- C \(\pm 2 i\)
- D \(5\)
Answer & Solution
Correct Answer
(A) \(-2\)
Step-by-step Solution
Detailed explanation
Given \(z = \dfrac{\lambda + 4i}{1 + \lambda i}\), where \(z \in R\). To ensure \(z\) is real, the imaginary part of \(z\) must be zero. Multiply the numerator and denominator by the conjugate of the denominator, \(1 - \lambda i\):…
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