Complex power complex
Which of the following option is a property of the sum of principal values of the 2 numbers, and , where ?
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1 solution
e^(iπ) =-1. [Euler's identity]
=> e^(iπ) = (i)^2 => e^(iπ/2)=i. [by taking square roots on both sides] => (e^(iπ))^i = i^i => e^(-π/2) = i^i => i^i = e^(-π/2). [ It is real] Similarly i^(-i) = e^(π/2). [It is also real] Therefore i^i +i^(-i) is also real.