Express the complex number in trigonometric form.

5 - 5i

Question

Express the complex number in trigonometric form. 

5 - 5i

anonymous · Answer

@hartnn

hartnn · Answer

a+bi <---> r (cos theta+i sin theta)

$r=\sqrt{a^2+b^2} \ \theta= \tan^{-1}(b/a)$

here, a = +5, b=-5

anonymous · Answer

r = sqrt(25 + 25), so r = sqrt 50
θ = tan^-1(-5/5) 
what else do i do, hart?

hartnn · Answer

simplify....
sqrt 50 =... ? 
tan^-1  (-1) = ...?

anonymous · Answer

r = 5sqrt2
θ = -pi/4

hartnn · Answer

correct! :)
lastly, 
cos (-pi/4) = cos (pi/4)
and sin (-pi/4) = - sin (pi/4)
so,
5 sqrt 2 (cos pi/4 - i sin pi/4)
got this ?

anonymous · Answer

5sqrt2(cos(pi/4) - i*sin(pi/4) I got it, but the options are 5sqrt2(cos(5pi/4) - i*sin(5pi/4) or
5sqrt2(cos(7pi/4) - i*sin(7pi/4)

hartnn · Answer

ok, -pi/4 = -pi/4 +2pi = 7pi/4
so, 5 sqrt 2 (cos 7pi/4 + i sin 7pi/4)

anonymous · Answer

Wow, thanks hart. you're a beast

hartnn · Answer

not actually, but thanks for the compliment :)
welcome ^_^