InterviewSolution
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InterviewSolution
| 1. |
Find the real part of `(1-i)^(-i)dot` |
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Answer» Let `z= (1-i)^(-i)`. Taking log on both sides, we have log `z = -I log_(e) (1-i)` `= -I log_(e)(sqrt(2)(cos.(pi)/(4)- i sin.(pi)/(4)))` `= - log_(e) (sqrt(2)e^((-ipi//4)))` `=-i[(1)/(2)log_(e)2 + log_(e) ^(-ipi//4)]` `= -i[(1)/(2)log_(e),2-(pi)/(4)]` `= -(i)/(2)log_(e)2-(pi)/(4)` `rArr z=e^(-pi//4)e^(-i(log2)2)` `rArr " "Re(Z) = e^(-pi//4) cos((1)/(2) log2)` |
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