Question

find the value of i^-1097​

Answer 1

Step-by-step explanation:

i^1097 = 1/(i^1097) =1/(i ^1096×i^1)

1096 is divisible by 4 then i^1096=1

then we can substitute the value of i^ 1096= 1 in to the question ,then the answer is :

1/(1×i)=1/i

we must write this into a+ib form .So we have to take the conjugate of i = -i and multiplying by this to the numerator and denomerator

= (1)/(i)×(-i)/(-i) that is,

= (1×(-i))/ ((i)× (-i)

= -i/(-i)²

= -i/1

= -i

Answer 2

SOLUTION

TO EVALUATE

$\displaystyle \sf{ {i}^{ - 1097} }$

EVALUATION

Here the given complex number is

$\displaystyle \sf{ {i}^{ - 1097} }$

We simplify it as below

$\displaystyle \sf{ {i}^{ - 1097} }$

$\displaystyle \sf{ = \frac{1}{{i}^{ 1097} } }$

$\displaystyle \sf{ = \frac{1}{{( {i}^{2} )}^{ 548}.i } }$

$\displaystyle \sf{ = \frac{1}{{( - 1 )}^{ 548}.i } }$

$\displaystyle \sf{ = \frac{1}{1 \times i } }$

$\displaystyle \sf{ = \frac{1}{i } }$

$\displaystyle \sf{ = \frac{i}{ {i}^{2} } }$

$\displaystyle \sf{ = \frac{i}{ - 1 } }$

$\displaystyle \sf{ = - i}$

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