Determine the roots in the following case :

i. Square roots of i

ii. Square roots of (1+i)

iii. Square roots of 1+sqrt(3) i

Total no hints on how to solve the problem. ANy idea ?

i. Square roots of i

ii. Square roots of (1+i)

iii. Square roots of 1+sqrt(3) i

Total no hints on how to solve the problem. ANy idea ?

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1. Assume the form of the answer, and equate the coefficients.

Every complex number has the form

number squared will be

For the first case:

Solve the two simultaneous equations for

2. Things get easier if you know about the polar representation

of complex numbers.

i = e^[i*pi/2 +i*2pi*k] for k = any integer.

Then i^[1/2] =

e^[i*pi/4 +i*pi*k] for k = any integer.

https://en.m.wikipedia.org/wiki/Euler%27s_identity#Imaginary_exponents

Letting k = 0 (although you can pick any integer value, but k = 0 is often chosen to keep the angle between 0 and 360 degrees):

```
i^[1/2] = e^[i*pi/4]
= cos pi/4 + i* sin pi/4
pi is 180 degrees, so pi/4 is 45 degrees.
cos 45 = sin 45 = 1/sqrt(2)
```

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