Question

Evaluate(i^17-(1/i)^34)^2

Answer 1

As i^4 = 1

answer is 2i

hope this will help you

Answer 2

Concept

Iota

Iota is an imaginary unit number symbolized by the letter I and its value is √-1.

Given

Given the expression $(i^{17}-(\frac{1}{i} )^{34})^2$.

Find

We have to Evaluate this expression.

Solution

First the values of $i^{17}$ and $(\frac{1}{i} )^{34}$

then,

$i^{17}=i^{16}\times i$

     $=(i^4)^4\times i$

     $=(1)^4\times i$

    $=i$

and

$\frac{1}{i^{34}} =\frac{1}{(i^{2})^{17}}$

    $=\frac{1}{(-1)^{17}}$

    $=-1$

Now substitute these value in $(i^{17}-(\frac{1}{i} )^{34})^2$.

then $(i^{17}-(\frac{1}{i} )^{34})^2=(i-(-1))^2$

                             $=(1+i)^2$

                             $=1+(i)^2+2i$

                             $=1-1+2i$

                             $=2i$

Hence the value is $2i$.