SOLUTION: Find a complex number a+bi such that radical i is equal to a+bi.
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Question 230237: Find a complex number a+bi such that radical i is equal to a+bi.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
We know that \ =\ 0)
and \ =\ 1)
, therefore we can say that:
\ +\ i\sin\left(\frac{\pi}{2}\right)\)
But we know from Euler's Formula that:
Hence:
}\ =\ i)
Taking the square root of both sides:
}\ =\ i^{\frac{1}{2}})
But
}\ =\ \pm\sqrt{i}\ =\ \cos\left(\frac{\pi}{4}\right)\ +\ i\sin\left(\frac{\pi}{4}\right)\)
Finally:
)
after rationalizing the denominators.
John
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