AP EAMCET · Maths · Complex Number
The value of \(\left\{i^{22}-\left(\frac{1}{i}\right)^{35}\right\}^2\) is
- A \(2 i\)
- B \(i\)
- C \(-i\)
- D \(-2 i\)
Answer & Solution
Correct Answer
(A) \(2 i\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{lr}\text { We have, }\left(i^{22}-\left(\frac{1}{i}\right)^{35}\right)^2 & \\ =(-1-i)^2 & {\left[\because i^{22}=i^{20} \times i^2=-\right]} \\ =(-1)^2+(-i)^2+2 i & {\left[\frac{1}{i^{35}}=\frac{i}{i^{36}}=i\right]} \\ =1-1+2 i=2 i & \end{array}\)
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