Why is the Square Root of Negative One equal to i?

Suffering from insomnia? Got 16 minutes to learn something new? Yes, the "principle square root" of negative 1 is i, however in search of the answer x²=-1, the quadratic nature of this problem will pose 2 possible correct answers, hence both i and -i are correct. Similarly, a cubic function x³=1 should have 3 possible roots. I suggest you try to figure out this answer using your newfound knowledge though this video before the spoiler alert down below. For more adventures like this, make sure you like, subscribe, and maybe leave a nice comment below to contribute :) www.patreon.com/scienceNme SPOILER ALERT!!! x³=1 has 3 possible roots. You can think of the answer as "What 3 same angles, if added together will equal a full circle?". So If you break a circle down into 3 equal parts, then: 1∠0° is a possible answer (1∠0° x 1∠0° x 1∠0° = 1∠0° = 1) 1∠120° is a possible answer (1∠120° x 1∠120° x 1∠120° = 1∠360° = 1) (1∠120° = - 0.5 + (√3)/2 i ) 1∠240° is a possible answer (1∠240° x 1∠240° x 1∠240° = 1∠720° = 1) (1∠240° = - 0.5 - (√3)/2 i ) And yes I know "x" is cross multiply. There is only so much that can be done though typing before the solution becomes too convoluted to interpret.

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