Question 1027375: Find all the roots of (sqrt -1), leave the answer in polar form.
Found 4 solutions by satyareddy22, Alan3354, ikleyn, greenestamps:
Answer by satyareddy22(84)   (Show Source):
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Find all the roots of (sqrt -1), leave the answer in polar form.
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-1 --> 1cis(180)
sqrt(-1) = 1cis(90) and 1cis(270)
Answer by ikleyn(53742)  (Show Source):
Answer by greenestamps(13325)  (Show Source):
You can put this solution on YOUR website!
In order to answer this question, we first have to try to guess what the real question is. The presentation of the problem is exceedingly bad.
To start with, we have to guess what the meaning is of "(sqrt -1)". This looks like an expression involving the subtraction of one number from another; but "sqrt" is not a number. So the only reasonable guess is that this is supposed to be "sqrt(-1)".
Next, the question asks us to find roots. Roots are solutions to an equation; but there is no equation anywhere in the statement of the problem. "sqrt(-1)" is a number; numbers do not have roots.
Another tutor APPEARS to have interpreted the question to be asking for the SQUARE roots of "sqrt(-1)", giving two answers. But in fact what she showed in her response was dangerously wrong. She said  has the two values of i and -i. But is A number -- it can't have two different values.
But the problem ask for "all" the roots of "sqrt(-1)", and while that number has two square roots, is also has three cube roots, and four 4th roots, and 93 93rd roots....
So the reader in the end has no idea what the question is really asking.
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