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Question

# Using the method of the earlier Example, find the quantities.$\sqrt{\sqrt{i}}$

Solution

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We are looking for a number $z$ such that $z=\sqrt{\sqrt{i}}.$ Notice that $\sqrt{\sqrt{i}}=\sqrt{i}.$ Therefore, we are looking for a $z$ such that

$z=\sqrt{i}.$

Rewriting the expression from above it yields that we are looking for a number $z$ such that

$z^4=i.$

Since $z$ is a complex number $z=a+bi$ it yields that:

$z^4=(a+bi)^4$

and hence

$(a+bi)^4=i.$

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