SOLUTION: i have been working on "i exponent 1/2" for a while. i think it is 0.5i since... rewrite as "i^1 over 2" remove the "exponent 1" "i over 2" is the same as 0.5i my problem

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You can't claim that . Instead, what you could do is rewrite i using Euler's formula (which is derived from Taylor series):



Then,






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Another way to do it is to say that





We can equate real and imaginary coefficients. The real part is a^2 - b^2 which is equal to 0 (since the real part of i is 0), so a^2 = b^2. Also, by equating the imaginary parts, 2ab = 1, so ab = 1/2. It follows that a = b = sqrt(2)/2 works (you can check as well), so



Update: Since a and b are real numbers, then the real part of the expression we are interested in is a^2 - b^2. If this is equal to i (think of it as 0+i), then a^2 - b^2 = 0 --> a^2 = b^2. The imaginary part of the expression is 2ab, which is equal to 1 (think, i = 2abi, 2ab = 1). Then solve for a and b.