How do you multiply $e^{\frac{π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

Question

How do you multiply $e^{\frac{π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

1 Answer

Impact of this question

1403 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-30T10:31:04

As $e^{i θ} = cos θ + i sin θ$ $e^(itheta)=costheta+isintheta$

$e^{\frac{π}{8} i} = cos (\frac{π}{8}) + i sin (\frac{π}{8})$ $e^(pi/8i)=cos(pi/8)+isin(pi/8)$ and

$e^{\frac{π}{2} i} = cos (\frac{π}{2}) + i sin (\frac{π}{2})$ $e^(pi/2i)=cos(pi/2)+isin(pi/2)$

and $e^{\frac{π}{8} i} \cdot e^{\frac{π}{2} i} = (cos (\frac{π}{8}) + i sin (\frac{π}{8})) (cos (\frac{π}{2}) + i sin (\frac{π}{2}))$ $e^(pi/8i)*e^(pi/2i)=(cos(pi/8)+isin(pi/8))(cos(pi/2)+isin(pi/2))$

= $cos (\frac{π}{8}) cos (\frac{π}{2}) + cos (\frac{π}{8}) \times i sin (\frac{π}{2}) + i sin (\frac{π}{8}) \times cos (\frac{π}{2}) + i sin (\frac{π}{8}) \times i sin (\frac{π}{2})$ $cos(pi/8)cos(pi/2)+cos(pi/8)xxisin(pi/2)+isin(pi/8)xxcos(pi/2)+isin(pi/8)xxisin(pi/2)$

= $cos (\frac{π}{8}) cos (\frac{π}{2}) + i cos (\frac{π}{8}) sin (\frac{π}{2}) + i sin (\frac{π}{8}) cos (\frac{π}{2}) + i^{2} sin (\frac{π}{8}) sin (\frac{π}{2})$ $cos(pi/8)cos(pi/2)+icos(pi/8)sin(pi/2)+isin(pi/8)cos(pi/2)+i^2sin(pi/8)sin(pi/2)$

= $cos (\frac{π}{8}) cos (\frac{π}{2}) + i cos (\frac{π}{8}) sin (\frac{π}{2}) + i sin (\frac{π}{8}) cos (\frac{π}{2}) - sin (\frac{π}{8}) sin (\frac{π}{2})$ $cos(pi/8)cos(pi/2)+icos(pi/8)sin(pi/2)+isin(pi/8)cos(pi/2)-sin(pi/8)sin(pi/2)$

= $[cos (\frac{π}{8}) cos (\frac{π}{2}) - sin (\frac{π}{8}) sin (\frac{π}{2})] + i [cos (\frac{π}{2}) sin (\frac{π}{8}) + sin (\frac{π}{2}) cos (\frac{π}{8})]$ $[cos(pi/8)cos(pi/2)-sin(pi/8)sin(pi/2)]+i[cos(pi/2)sin(pi/8)+sin(pi/2)cos(pi/8)]$

= $cos (\frac{π}{8} + \frac{π}{2}) + i sin (\frac{π}{8} + \frac{π}{2})$ $cos(pi/8+pi/2)+isin(pi/8+pi/2)$

= $e^{\frac{π}{8} + \frac{π}{2}}$ $e^(pi/8+pi/2)$

Science

Math

Humanities

... and beyond

How do you multiply $e^{\frac{π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you multiply eπ8i⋅eπ2ie^(( pi )/ 8 i) * e^( pi/2 i ) in trigonometric form?

1 Answer

Related questions

Impact of this question

How do you multiply $e^{\frac{π}{8} i} \cdot e^{\frac{π}{2} i}$ $e^(( pi )/ 8 i) * e^( pi/2 i )$ in trigonometric form?