Question

Find all the values of (-i) 1/6
​

Answer 1

values of (-i) 1/6 is Cos π/4 + i sinπ/4 Or 1/√2 + i 1/√2.​

given :

(-i) 1/6

To find :

value

Solution:

We know, Demoiveis theory is  = cosФ + isinФ= c ^ iФ

Z= ( Ф - i) ^1/6

= {Ф+(-1)i} ^1/6                                           { If, cosФ = 0 sin Ф = _1

                                                                    So, there Ф = 3π/2}

we get,  cos 3π/2 + isin 3π/2) ^1/6

Apply Demoiveis theory ,

(e^i3π/2)^^1/6

We know, e^m = emn

e ^ i( 3π/2 * 1/6)

e ^ i π/4

so, we get ,

Cos π/4 + i sinπ/4

Or 1/√2 + i 1/√2

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