AP EAMCET · Maths · Complex Number
The product of the four values of the complex number \((1+i)^{3 / 4}\) is
- A \(2(1+i)\)
- B \(2(1-\mathrm{i})\)
- C \(2^3(1+i)\)
- D \(2^3(1-i)\)
Answer & Solution
Correct Answer
(B) \(2(1-\mathrm{i})\)
Step-by-step Solution
Detailed explanation
Let the complex number be \(z = (1+i)^{3/4}\). The product of the \(n\) roots of a complex number \(w\) is given by \( (-1)^{n-1} w \). Here, \(w = (1+i)^3\) and \(n=4\). Product \(= (-1)^{4-1} (1+i)^3 \) \(= (-1)^3 (1+i)^3 \) \(= -(1+i)^3 \)…
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