hi guys,

I am wondering how come cos(theta)+i sin(theta) == x +yi

Could you please explain me? with one example please

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- Apr 3rd 2011, 08:43 AMprobladyquestion about complex plane
hi guys,

I am wondering how come cos(theta)+i sin(theta) == x +yi

Could you please explain me? with one example please - Apr 3rd 2011, 08:53 AMPlato
- Apr 3rd 2011, 09:01 AMproblady
Yes I know about polar coordinates! So please explain...

- Apr 3rd 2011, 09:11 AMPlato
- Apr 3rd 2011, 09:15 AMproblady
Thanks dear!

- Apr 3rd 2011, 11:04 AMHallsofIvy
Another way of looking at it: from the point (x, y) in the coordinate plane, draw a perpendicular to the x-axis. That, the x-axis itself, and the line from (x,y) to the origin, which has length $\displaystyle r= \sqrt{x^2+ y^2}$ make a right triangle. The "opposite side", parallel to the y-axis, has length $\displaystyle y= r sin(\theta)$ and the "near side", along the x-axis, has length $\displaystyle x= rcos(\theta)$.

The standard convention for representing complex numbers as points in the plane, sets the imaginary part of the number to the y-coordinate and the real part to the x-coordinate. That gives $\displaystyle x+ iy= r cos(\theta)+ i r sin(\theta)$. Of course, your example, [itex]x+ iy= cos(\theta)+ i sin(\theta)[/itex], implies that [itex]r= |x+ iy|= 1[/itex]