Finding Square Roots of i | Complex Numbers

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[DrWizardMother]

Complex numbers became a lot easier when I gained enough intuition to know that i is just a rotation by pi/2. So...root(i) is any rotation that performed twice gives a rotation that ends on the imaginary axis...AND has magnitude unity. Using polar coordinates makes it easier to get a closed form in this way also.

[MathOrient]

Using polar coordinates is the easiest.

[migry]

I'm no mathematician, but I simply visualised the polar graph and a line bisecting the x and y axis, length 1, then I just needed to figure x and y. My interest is seeing a line length 1 sweeping around the 0, 0 point and making a sine/cosine wave, which is useful for maths associated with radio circuits.

[bjorntorlarsson]

Define epsilon = 1/0 and have a look at that! When you encounter x/0, call it x*epsilon and perhaps you can get rid of the epsilon part later. How does that differ from defining i=sqrt(-1)?

[robertveith]

*@ SyberMath* -- In your 2nd method, sqrt(2i) does not equal 1 + i or -1 - i. sqrt(i) = i, but
- sqrt(i) = -1 - i.

[alextang]

It is very easy to solve by turning right hand side i into polar form. 😋😋😋😋😋😋

[srividhyamoorthy]

I already saw brbp video for value of root i lol