Question 523689: 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 is that i need to begin with an "a+bi" format then raise both sides to remove the exponent. then i should be left with an answer.
thank you
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! 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
^2 = a^2 + 2abi - b^2 = (a^2 - b^2) + 2abi)
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.
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