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Homework Help: Converting a number to rectangular form

  1. Mar 14, 2008 #1
    Find the rectangular form of the complex number z=a+bi which has modulus 2 and principal argument theta = -pie/6
    2cos(-pie/6) to get length of x
    =sqrt3 What is the method used to get an answer in this form instead of decimal form (1.732) ?
     
  2. jcsd
  3. Mar 14, 2008 #2

    rock.freak667

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    Use Euler's formula
     
  4. Mar 14, 2008 #3
    Could you please show me the steps?
     
  5. Mar 14, 2008 #4

    Dick

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    The complex number with modulus r and argument theta is r*exp(i*theta)=r*(cos(theta)+i*sin(theta)). exp(i*theta)=cos(theta)+i*sin(theta) is Euler's formula.
     
  6. Mar 14, 2008 #5
    Isn't there a quicker way to do it?
     
  7. Mar 14, 2008 #6

    Dick

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    ?? If you followed that then the real part of z is x=r*cos(theta)=2*cos(-pi/6). What do you mean 'quicker'. I just wrote it down. I didn't compute anything. How could anything else be quicker?
     
  8. Mar 14, 2008 #7
    I have that in my initial post. I was just wanting to know how u get sqrt3 instead of 1.732.
     
  9. Mar 14, 2008 #8

    Dick

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    Oh. Sorry. Draw an equilateral triangle with side 1. Then pi/6 is half of one of the angles (since they are all pi/3). So split the equilateral triangle into two right triangles with base 1/2 and hypotenuse 1. The remaining side is sqrt(3)/2. Use pythagoras. cos(pi/6) is that remaining side over the hypotenuse. So cos(pi/6)=sqrt(3)/2. So 2*cos(pi/6)=sqrt(3). Misunderstood your question.
     
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