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Converting a number to rectangular form

  • Thread starter Ry122
  • Start date
565
2
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) ?
 

Answers and Replies

rock.freak667
Homework Helper
6,230
31
Use Euler's formula
 
565
2
Could you please show me the steps?
 
Dick
Science Advisor
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26,258
618
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.
 
565
2
Isn't there a quicker way to do it?
 
Dick
Science Advisor
Homework Helper
26,258
618
?? 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?
 
565
2
I have that in my initial post. I was just wanting to know how u get sqrt3 instead of 1.732.
 
Dick
Science Advisor
Homework Helper
26,258
618
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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