AP EAMCET · Maths · Complex Number
By simplifying \(i^{18}-3 i^7+i^2\left(1+i^4\right)(i)^{22}\), we get
- A \(-1+3 i\)
- B \(1-3 i\)
- C \(1+3 i\)
- D \(-1-3 i\)
Answer & Solution
Correct Answer
(C) \(1+3 i\)
Step-by-step Solution
Detailed explanation
\(i^{18}-3 i^7+i^2\left(1+i^4\right)(i)^{22}\) \(=i^{4 \times 4+2}-3 i^{4+3}+-1(1+1)\left(i^2\right)^{11}\) \(=i^2-3 i^3+2 \quad\left[\because i^2=-1\right.\) and \(\left.i^4=1\right]\) \(=-1+3 i+2=1+3 i\)
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