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# How does the sqaure root of -1 = i?

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Can some explain to me how:

$${\sqrt{-{\mathtt{1}}}} = {i}$$

and how do you work out the sqaure root of -1?

NathanDeAlien  Nov 30, 2014

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Ok thanks!

NathanDeAlien  Nov 30, 2014
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Hi Nathan,

i is the basic unit of the imaginary number system.

Nothing multiplied by itself can be negative.  That is impossible in the REAL world.

So    $${\sqrt{-{\mathtt{1}}}}$$    does not exist in the real world.

BUT there is a whole other system of numbers called imaginary OR complex numbers and in that system

$${\sqrt{-{\mathtt{1}}}}$$     is assigned the letter  $${i}$$

Melody  Nov 30, 2014
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