How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{5 π}{3} i}$ $e^( ( 7 pi)/4 i) - e^( ( 5 pi)/3 i)$ using trigonometric functions?

Question

How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{5 π}{3} i}$ $e^( ( 7 pi)/4 i) - e^( ( 5 pi)/3 i)$ using trigonometric functions?

1 Answer

Impact of this question

1319 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-20T16:07:15

$0.207 + 0.159 i$ $0.207+0.159i$

Explanation:

Euler's Theorem states that $e^{i θ} = cos θ + i sin θ$ $e^(itheta)=costheta+isintheta$ .

Application of this theorem to the given question yields

$cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4}) - (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3}))$ $cos((7pi)/4)+isin((7pi)/4)-(cos((5pi)/3)+isin((5pi)/3))$

$= \frac{1}{\sqrt{2}} - \frac{1}{\sqrt{2}} i - 0.5 + 0.866 i$ $=1/sqrt2-1/sqrt2i-0.5+0.866i$

$= 0.207 + 0.159 i$ $=0.207+0.159i$

Science

Math

Humanities

... and beyond

How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{5 π}{3} i}$ $e^( ( 7 pi)/4 i) - e^( ( 5 pi)/3 i)$ using trigonometric functions?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you evaluate e7π4i−e5π3i e^( ( 7 pi)/4 i) - e^( ( 5 pi)/3 i) using trigonometric functions?

1 Answer

Explanation:

Related questions

Impact of this question

How do you evaluate $e^{\frac{7 π}{4} i} - e^{\frac{5 π}{3} i}$ $e^( ( 7 pi)/4 i) - e^( ( 5 pi)/3 i)$ using trigonometric functions?