TRIGONOMETRY
posted by Kate on .
Can someone please show me step by step how to calculate the modulus and the argument for these complex numbers? I have a trig final next week and I am trying to finish this study guide so I am prepared. Thank you so much! If you can, please show my how you get the answer so I actually learn something. :)
a) 5 + 5i
b) 5
c)3 4i

think back to your polar coordinates. Same thing.
(a+bi) = r cisθ
where
tanθ = y/x
r^2 = a^2 + b^2
5+5i
r^2 = 5^2+5^2, so r=5√2
tanθ = 5/5 = 1
Now, cosθ=x/r sinθ=y/r
since x<0 and y>0, θ is in II, so
θ = 3π/4
5 = 5+0i = 5 cis π
34i = 5 cis π+arctan(4/3)
because we are in QIII