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

1 answer

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

-3-4i = 5 cis π+arctan(-4/-3)
because we are in QIII
Similar Questions
    1. answers icon 1 answer
    1. answers icon 1 answer
  1. A student solves the following equation:Problem: 2(x−3)+3x=19 Step 1: 2x−6+3x=19 Step 2: (2x+3x)−6=19 Step 3: 5x−6=19
    1. answers icon 1 answer
  2. A student solves the following equation:Problem: 2(x−3)+3x=19 Step 1: 2x−6+3x=19 Step 2: (2x+3x)−6=19 Step 3: 5x−6=19
    1. answers icon 1 answer
more similar questions