Find the square root of i
When dealing with powers of complex numbers, always start by putting the quantity into exponential form.
i has a magnitude of 1 and an argument of π/2. Using Euler's formula,
i = exp(iπ/2)
Now the expression is in exponential form, taking the square root is easy, using basic exponential math.
sqrt(i) = (exp(iπ/2))^(1/2) = exp(iπ/4)
This quantity has a modulus of 1 and an argument of π/4. Using Euler's formula again,
sqrt(i) = (1 + i)/sqrt(2)
JL
Answered by Jamie L. • Further Mathematics tutor
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