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
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.

 

[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 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 on both sides?

<br /> You need to terminate it.
2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2}

 

[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 on both sides?

<br /> <br /> In your original submission (still echoed in the panel above my response) you will see that you used &quot;[ tex ] some math [ /tex ]&quot;. The spaces you inserted inside [...] were a mistake: you should have &quot;[t..x] some math [/t..x]&quot; , where &#039;..&#039; means &#039;e&#039;. The rest of your expression was perfectly OK.