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Question

Using the method of the earlier Example, find the quantities.

i\sqrt{\sqrt{i}}

Solution

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Answered 1 year ago
Answered 1 year ago
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We are looking for a number zz such that z=i.z=\sqrt{\sqrt{i}}. Notice that i=i4.\sqrt{\sqrt{i}}=\sqrt[4]{i}. Therefore, we are looking for a zz such that

z=i4.z=\sqrt[4]{i}.

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

z4=i.z^4=i.

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

z4=(a+bi)4z^4=(a+bi)^4

and hence

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

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