We will find both the square roots of i, i.e. sqrt(i). We will first write sqrt(i) as a complex number a+bi and then square both sides. Then we will solve for a and b by setting a system of equations! This is the algebra way to find the square root of the imaginary unit i.

Check out these related videos:
polar way:    • sqrt(i) in polar form  
sqrt(i+sqrt(i+sqrt(i+...))):    • sqrt(i+sqrt(i+sqrt(i+...))) = ?  

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