InterviewSolution
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InterviewSolution
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Evaluate : (i) `i^(135)` (ii) `i^((1)/(47)` (iii) `(-sqrt(-1))^(4n +3) , n in N` (iv) `sqrt(-25) + 3sqrt(-4) + 2 sqrt(-9)` |
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Answer» (i) 135 leaves reaminder as 3 when it is divided by 4. Therefore, `i^(135) = i^(3) = - i` (ii) `i^((1)/(47)) = (1)/(i^(44)i^(3)) = (1)/(-i^(2))=i` (iii) `(-sqrt(-1))^(4n + 3) = (-i)^(4n + 3)` ` =(-i)^(4n) (-i)^(3)` `= {(-i)^(4n) } (-i)^(3)` `= 1 xx (-i)^(3) = - i^(3) = -i^(3) = - (-i)=i` (iv) `sqrt(-25) + 3sqrt(-4) + 2 sqrt(-9) = 5i + 6 i + 6i = 17i` |
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