Question

express i^109 in the form of
a + ib​

Answer 1

SOLUTION

TO EXPRESS

$\sf{ {i}^{109} \: \: in \: form \: of \: a + ib }$

EVALUATION

Here the given equation complex number is

$\sf{ {i}^{109} }$

We simplify it as below

$\sf{ {(i)}^{109} }$

$\sf{ = {(i)}^{108} \times i}$

$\sf{ = {( {i}^{2} )}^{54} \times i}$

$\sf{ = {( - 1 )}^{54} \times i}$

$\sf{ = 1 \times i}$

$\sf{ = i}$

Which is of the form a + ib

Where a = 0 & b = 1

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