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How do i find the principal form of this complex number 
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#1
Dec1412, 03:35 AM

P: 79

z= (10^{j}+e^{logj})^{2}
I tried expanding but it just made it more complicated. help please!! 


#2
Dec1412, 03:44 AM

P: 79

the principal form is defined in my book as
ln(z)=ln(r)+jθ 


#3
Dec1412, 01:47 PM

HW Helper
P: 6,188

To find the principal form you need to find the length and the angle of z. First step is to find the length and angle of 10^{j}. And also of e^{logj}. Do you know how? 


#4
Dec1512, 02:20 AM

P: 79

How do i find the principal form of this complex number
How?
That's exactly what my problem is. 10^{j} and e^{logj} aren't similar to any of the forms discussed in school. Can you give another hint? 


#5
Dec1512, 10:18 AM

HW Helper
P: 6,188

Let's try and find ln(z)=ln(r)+jθ for 10^{j} and for e^{logj}.
ln(10^{j}) = j ln(10) = ln(1)  j ln(10) So what is the length r and what is the angle θ for 10^{j}? Let's break e^{logj} apart a little further. First we look at "j". Did you know that "j" has length 1 and angle pi/2? In other words, we have: $$j = e^{j {\pi \over 2}}$$ Can you take the log of j? And if so, find the length and angle of e^{logj}? 


#6
Dec1712, 03:41 AM

P: 79

thanks!!



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