COMEDK · Maths · 3. Complex Number
Evaluate \(\left[i^{18}+\left(\dfrac{1}{i}\right)^{25}\right]^{3}\).
- A \(2(1-i)\)
- B \(7(i-1)\)
- C \(2-7 i\)
- D \(8 i+4\)
Answer & Solution
Correct Answer
(A) \(2(1-i)\)
Step-by-step Solution
Detailed explanation
\(i^{18} = i^{16} \cdot i^2 = 1 \cdot (-1) = -1\) \(\dfrac{1}{i} = \dfrac{i}{i^2} = \dfrac{i}{-1} = -i \Rightarrow \left(\dfrac{1}{i}\right)^{25} = (-i)^{25} = (-1)^{25} \cdot i^{25} = -1 \cdot i^{24} \cdot i = -i\)…
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