Solving e^z=w in Polar Form | Abs(right hand side)=2 without ln 2 in Solution

[Dousin12]

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?

 

[Ray Vickson]

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
[tex] 2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2}[/tex]
Anyway, the absolute value of the rhs is not 2.

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

 

[Dousin12]

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]

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.

 

[Dousin12]

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?

 

[SammyS]

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 [/tex] to terminate it.
[tex]2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2}[/tex]

 

[Ray Vickson]

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?

In your original submission (still echoed in the panel above my response) you will see that you used "[ tex ] some math [ /tex ]". The spaces you inserted inside [...] were a mistake: you should have "[t..x] some math [/t..x]" , where '..' means 'e'. The rest of your expression was perfectly OK.