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Finding modulus and argument of a complex number 
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#1
Jan1409, 05:50 PM

P: 32

1. The problem statement, all variables and given/known data
Find the modulus and argument of z=1cos(a)i*sin(a) 2. Relevant equations mod(z)=sqrt(a^2+b^2) 3. The attempt at a solution mod(z)=sqrt((1cos(a))^2+(sin(a))^2) =sqrt(22cos(a)) arg(z)=arctan((sin(a))/(1cos(a))) This is as far as I can get, I have asked my math teacher but he is not very familiar with thise. my textbook gives mod(z) as 2sin(2a) and arg(z) as (api)2 BTW this question is from the IB math textbook, there exists a solutions manual but I do not have it... the question is 11.2, 19 a) Thanks in advance! 


#2
Jan1409, 06:00 PM

Sci Advisor
HW Helper
Thanks
P: 26,148

Hi choob!
You need to learn your trigonometric identities … in this case, sin = 2 sin1/2 cos1/2 and 1  cos = 2 sin^{2}1/2 


#3
Jan1409, 06:47 PM

P: 32

i can get arg(z) to arctan(cos(a/2)/(sin a/2)), how do i finish this?



#4
Jan1409, 06:58 PM

HW Helper
P: 6,202

Finding modulus and argument of a complex number
This will help you.
[tex]tan(\frac{\pi}{2}\theta)= \frac{1}{tan\theta}[/tex] 


#5
Jan1409, 08:19 PM

P: 32

wow thanks a lot, lol.



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