How do you evaluate $e^( ( 7 pi)/4 i) - e^( ( 8 pi)/3 i)$ using trigonometric functions?

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Answer 1 · 2016-05-03T09:23:22

$0.881-1.692i$

According to Euler's formula,

$e^(ix)=cosx+isinx$

If we substitute in values for $x$ from the question, we get

$e^((7pi)/4i)=cos((7pi)/4)+isin((7pi)/4)$
$=cos315+isin315$
$=0.707-0.707i$

$e^((8pi)/3i)=cos((8pi)/3)+isin((8pi)/3)$
$=cos100+isin100$
$=-0.174+0.985i$

Now you have the two parts of the question, you put them together and solve arithmetically:

$e^((7pi)/4i)-e^((8pi)/3i)$
$=(0.707-0.707i)-(-0.174+0.985i)$
$=0.707+0.174-0.707i-0.985i$

$=0.881-1.692i$

How do you evaluate e^( ( 7 pi)/4 i) - e^( ( 8 pi)/3 i) e^( ( 7 pi)/4 i) - e^( ( 8 pi)/3 i) using trigonometric functions?