what is √-i where i=√-1 equal to?
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Answered by
2
Answer:
Step-by-step explanation:
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nick6018:
but according to answer key 2 is in denominator
Maybe they have "rationalized the denominator". So instead of 1/root2, they might have (root2)/2 which is the same thing.
Don't forget ( -1 + i ) / root2 as well!
well the ans is misprinted.. thanks
Answered by
2
Answer:
± ( 1 - i ) / √2
= ±√2 ( 1 - i ) / 2
Step-by-step explanation:
To see this, just square it.
[ ± ( 1 - i ) / √2 ]²
= ( 1 - i )² / 2
= ( 1 + i² - 2i ) / 2
= ( 1 - 1 - 2i ) / 2
= -2i / 2
= -i
Basically, what's going on is that multiplication is rotation and dilation.
So -i = -i × 1 corresponds to rotating 1 clockwise by 90°.
For a "square root", we need a number z such that z² = -i. That it, starting with 1 and then applying the rotation z twice should be the same as rotating clockwise 90°.
Well, rotating clockwise 45° does that! Do that twice and you've rotated 90°.
Also, rotating clockwise (180+45)° has the same effect.
These are the two values for z such that z² = -i.
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