Q. Trig/Polys/Complex Numbers (1 Viewer)

[ezzy85]

ive got x= cos@ + isin@ to bea root of an equation.

i know that:
cos@ = 3/5
cos@ = 1/2

i have to find x. the second one is easy. i just found the angles and subbed them back into x. but with the first one you dont get a nice angle. how would you sub it in? the answer is 3/5 + 4/5i. how did they get it in such a "nice" form?
Thanks

 

[spice girl]

use the fact that (cos@)^2 + (sin@)^2 = 1

 

[BlackJack]

They've just used the pythagoras triangle, with the opposite, adjacent, hypotenuse ratios. THe angle wasn't required.

cos@ = a / h (is 3/5)

sin@ = o / h
(is 4/5, o^2 = h^2 - a^2 = 5^2 - 3^2...)

 

[ezzy85]

of course.
Thanks for that