InterviewSolution
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InterviewSolution
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What is `((sqrt(3)+i)/(sqrt(3)-i))^(6)` equal to, where `I = sqrt(-1)` ?A. 1B. `1//6`C. 6D. 2 |
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Answer» Correct Answer - A `((sqrt(3)+i)/(sqrt(3)-i))=(sqrt(3)+i)/(sqrt(3)-i)xx(sqrt(3)+i)/(sqrt(3)+i)` `(3+i^(2)+2 sqrt(3)i)/(3-i^(2))=(3-1+2 sqrt(3)i)/(3+1)` `=(2(1+sqrt(3)i))/(4)=(1)/(2)+i(sqrt(3))/(2)` `=("cos"(pi)/(3)+"i sin"(pi)/(3))=e^(i(pi)/(3)` `therefore ((sqrt(3)+i)/(sqrt(3)-i))^(6)=(e^(i(pi)/(3)))^(6)=e^(i2pi)cos 2 pi + i sin 2 pi` `= 1 + 0.i = 1` |
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