Writing in polar form a complex number

  • Thread starter homevolend
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  • #1
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Homework Statement



Write z = 1 + √3i in polar form

Homework Equations



z = r (cos[itex]\varphi[/itex] + sin[itex]\varphi[/itex]i)

The Attempt at a Solution



Found the modulus by

|z| = √4 = 2

Now I am stuck on this part of finding the argument:

Tan-1 (√3)

now I am not sure how to go from that to the ans which is pi/3.



So would be:?

z= 2(cos(Tan-1 (√3)) + sin(Tan-1 (√3))i)
 

Answers and Replies

  • #2
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when i was in complex, the unit circle became my best friend. look at the unit circle, and think about the point that z would make on the unit circle.
 
  • #3
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√3 / 2 would be the y coordinate of pi/3.

Just not sure how that coordinate can make the argument pi/3?
 
  • #4
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well, the angle pi/3 gives you √3/2, correct? And you're multiplying on the outside by 2, right?

what's cos of the same angle?

you're using a different way to make your point. So you need angles to do it in the polar form.

If you memorize 3 or 4 pairs from the unit ciricle, I think, you can figure out most common forms of numbers they give you. Unless they're being sneaky, they usually give nice proportions of pi to make pretty numbers.
 
  • #5
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another way of thinking about this is, what is tangent? sin over cosine. so there needs to be some argument such that sin(x)/cos(x) =√3. So look at the unit circle. what arguments involve the root of 3? π/6 does, but tan of π/6=sin(π/6)/cos(π/6)=1/√3. What else does? π/3. now what do you get?
 

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