# Equation of e^z=w form

## Homework Statement

$$2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2}$$
Then i write the right side as polar form and the abs(right hand side)=2 , and then multiplied with an angle. But in the answer there is only pi/4*i. which is the angle i get, but since the abs(right hand side)=2, why isn't there a "ln 2" in the solution?

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Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

[ tex ] 2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2}\\ [ /tex ]
Then i write the right side as polar form and the abs(right hand side)=2 , and then multiplied with an angle. But in the answer there is only pi/4*i. which is the angle i get, but since the abs(right hand side)=2, why isn't there a "ln 2" in the solution?

Please write your TeX/LaTeX properly; I have fixed up the above and have obtained
$$2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2}$$
Anyway, the absolute value of the rhs is not 2.

Mod note: I fixed the contents of the original post.

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Yeah i saw when i went to bed, :D My bad. I wrote wrong on the calculator

Btw how do i write latex properly? I can't figure out how to do it!

haruspex
Homework Helper
Gold Member
Yeah i saw when i went to bed, :D My bad. I wrote wrong on the calculator

Btw how do i write latex properly? I can't figure out how to do it!
If you right click on the equations Ray posted you should see an option to display the latex.

2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2}

this is what i see,

HOw to i get it to be latex? I thought just write $$on both sides? SammyS Staff Emeritus Science Advisor Homework Helper Gold Member 2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2} this is what i see, HOw to i get it to be latex? I thought just write [tex] on both sides? You need$$ to terminate it.
$$2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2}$$

Ray Vickson