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TRIGONOMETRY

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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

  • TRIGONOMETRY -

    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

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