anonymous
  • anonymous
How do I use polar form to determine z1z2 if z1= -√3 + i, z2 = -3-3i?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Here's what i have so far: Z1Z2 = (-√3 + i)(-3-3i) = 3√3 + 3√3 i - 3i - 3i^2 = 3√3 + (√3-1)3i - 3(-1) = 3√3 + (√3-1)3i + 3
anonymous
  • anonymous
I know that polar form is: Z = r(costheta + isintheta)
anonymous
  • anonymous
I solved r1 and r2 through √(x^2+y^2) and got r1 = 2 and r2 = 3√2

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anonymous
  • anonymous
but I'm stuck with the cosine and sine part: costheta = x/r = (-√3)/2
anonymous
  • anonymous
how can I calculate theta without using a calculator? :$
UnkleRhaukus
  • UnkleRhaukus
\[z=a+ib\] the modulus is \(r=\sqrt{a^2+b^2}\) the argument is \(\theta=\arctan\frac ba\) \[z=re^{i\theta}\]
anonymous
  • anonymous
without using the calculator how would I calculator θ=arctanb/a?
UnkleRhaukus
  • UnkleRhaukus
well you can draw a triangle
UnkleRhaukus
  • UnkleRhaukus
|dw:1378697287188:dw|
UnkleRhaukus
  • UnkleRhaukus
|dw:1378697322981:dw|
UnkleRhaukus
  • UnkleRhaukus
\[\|dw:1378697396585:dw|theta\]

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