I keep googling it and I still don’t understand what they are and their differences 😭😭
In: 18
Real roots have no imaginary component, non real roots can have imaginary components
An example. The 4th roots of 1. You can multiply 1•1•1•1 to get 1. You can also multiply -1•-1•-1•-1 to get 1. Those are real roots.
Then there’s also i•i•i•i = 1 and -i•-i•-i•-i = 1 which are non real roots
An easy way to solve for all of them is polar form. Say you want to find the cube roots of 1. Well the polar form is 1∠0 which is equal to 1∠360 which is equal to 1∠720 (you can keep going, but you’ll just get repeated answers in further steps since we’re using the cube root which will have 3 roots)
Take those, and since it’s the cube root which is the third power, divide all of those angle by 3. You’ll end up with 1∠0 ; 1∠120 ; and 1∠240. If the angle is 0 or 180 it is a real root, if it is 90 or 270 it is a purely imaginary root, and anything else is a complex root. The way you get the final answer is converting the polar coordinates back to rectangular. So 1∠0 becomes 1•(cos(0) + sin(0) • i) = 1 {real root}; 1∠120 becomes 1•(cos(120) + sin(120) • i) = -0.5 + 0.866i; And 1∠240 becomes 1•(cos(240) + sin(240) • i) = -0.5 – 0.866i {both complex roots}
The reason it would repeat if you kept going is because if you go to 1∠1080 and divide 1080 by 3, you get 360 and 1∠0 would be equal to 1∠360 and just give you 1 again as a final answer
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