How can you use trigonometric functions to simplify $2 e^{\frac{π}{4} i}$ $2 e^( ( pi)/4 i )$ into a non-exponential complex number?

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Answer 1 · 2015-12-30T05:13:40

$\sqrt{2} (1 + i)$ $sqrt(2) (1+i)$

$e^(i Theta) = cos(Theta) + i sin(Theta)$

Therefore:
$2e^(pi/4 i) = 2(cos(pi/4) + i sin(pi/4))$

= $2(1/sqrt(2) + i 1/sqrt(2))$
= $2((sqrt(2) + i sqrt(2))/2)$
= $sqrt(2) (1 + i)$

How can you use trigonometric functions to simplify 2 e^( ( pi)/4 i ) 2eπ4i 2 e^( ( pi)/4 i ) into a non-exponential complex number?