1. ## Complex number(logarithm)

Let z = 4e^i(pi/6)
find iz and |e^iz|

what is iz?
is it imaginary part of z?

2. Originally Posted by nameck
Let z = 4e^i(pi/6)
find iz and |e^iz|

what is iz?
is it imaginary part of z?
I would assume so. Can you do that part?

For the second part note that

$\displaystyle \left|z\right|=\sqrt{\Re^2(z)+\Im^2(z)}$ and since $\displaystyle \Re\left(e^{iz}\right)=\cos(z),\Im\left(e^{iz}\rig ht)=\sin(z)$ it follows that $\displaystyle \left|e^{iz}\right|=\sqrt{\sin^2(z)+\cos^2(z)}=1$. Another way to realize this is that $\displaystyle e^{iz}$ is some point $\displaystyle \zeta$ on the unit circle. Thus $\displaystyle \left|e^{iz}\right|$ is the length of the radius $\displaystyle \overline{O\zeta}$, but since this is the unit circle this is trivially one.

3. got it for the second part.. what is the method to slove the first part?

4. Originally Posted by nameck
got it for the second part.. what is the method to slove the first part?
As I said $\displaystyle \Im\left(e^{iz}\right)=\sin\left(z\right)$. What's $\displaystyle z$?

5. Originally Posted by nameck
Let z = 4e^i(pi/6)
find iz and |e^iz|

what is iz?
is it imaginary part of z?
That would not be my interpretation! iz is just what it looks like: i times z.

You could either write z in "rectangular form", a+ bi, and then iz= -b+ ai, or write i in polar form, $\displaystyle e^{i\pi/2}$ and multiply $\displaystyle 4e^{i\pi/6}e^{i\pi/2}$.