$z^n=|z|^ne^{in\phi}=|z|e^{-i\phi}=\bar{z}$ $|z|^n=|z| \ \ \ \ \ \ \ \ \ $and $\ \ \ \ \ \ \ \ \ e^{in\phi}=e^{-i\phi}$  $|z|^{n-1}= 1 \ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n=\frac{-\phi}{\phi}=-1$  How to continue?
$$\overline{z}=z^n$$ where $n\in \mathbb{N}$   So I have started with moving the polar representation as the expression is in the n-th power  $$rcis(-\theta)=r^ncis(n\theta)$$   I can not multiply both sides in $r^{(-n)}$ as $n\in \mathbb{N}$ how should I continue?
Installing grounded light fixture on box with no ground conductor I'm installing a brand new motion activated security light to an existing box on my garage. After removing the old light, I notice it only has white/black wiring while the new light fixture has of course white/black/green (ground) wires to attach. What do I do if no ground wire is available with the old box? MySQL SELECT LAST_INSERT_ID() for compound key. Is it possible? Can I get the LAST INSERT ID() for a compound key in MySQL? How to sync bookmarks across Google Chrome and Mozilla Firefox bookmarks? Prove: if $a,b\in G$ commute with probability $>5/8$, then $G$ is abelian Suppose that $G$ is a finite group. If $P( ab=ba ) &gt;5/8$, prove $G$ is abelian. How do I print my Java object without getting "SomeType@2f92e0f4"? Interpret geometrically the equation The function $f$ is convex when:  $$f(tx+ (1-t)x', ty + (1-t)y') ≤  tf(x,y) + (1-t)f(x', y')$$  for all numbers $0≤t≤1$ and all pairs of points $(x,y)$ and $(x',y')$ in the domain of $f$ (the whole of $R^2$)  How would I interpret this geometrically? Also what is an example of a convex function whose graph is not a plane? I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful.  Is there any good examples of their uses outside academia? How to programmatically send SMS on the iPhone? Can I preemptively pay my credit card bill before a charge is posted? Getting started with neural networks for forecasting How to get text from an element , when getText fails I have the following element element(by.css(&quot;span[aria-label='Picker ID, TESTUSER']&quot;)  I want to assure the text on this filed is TESTUSER, so I tried:  expect(element(by.css(&quot;span[aria-label='Picker ID, TESTUSER']&quot;)).getAttribute('value')).toEqual('TESTUSER');  then I got the error: Expected null to equal 'TESTUSER' So I tried: element(by.css(&quot;span[aria-label='Picker ID, TESTUSER']&quot;)).getText().then(function (value) {         console.log(value);       })  And I got this error: Expected '' to be 'TESTUSER'.  How to get the value of this field and expect it is TESTUSER? I am creating an animated sprite list in Adobe Illustrator. I finished creating the sprites and used the Horizontal/Vertical Distribute Center commands to distribute the objects equally in some area.  But, if the objects are spread too far apart, the Distribute Center tool leaves, albeit equal, much distance between the objects. The opposite is true: if the objects are too close then distributing them will just overlap them.  My question is, is there any tool that just puts objects side by side?  I imagine that this tool would work if the objects aren't even equal in size.   I have viewed  and answer but it is not what I need. I'm having trouble with the OpenLayers Plugin of Qgis and the map composer:  If I create an OSM-background layer and if I want to export this, the OSM-Layer looks perfectly all right in the normal qgis program window. But in the map composer and after export the layer has shifted relatively to my other shape layers (EPSG:32633 - WGS 84 / UTM zone 33N).  The second thing is that the output resolution of the exported osm-layer is very, very poor.   A really bad way of getting around this whole trouble would be to increase the screen resolution and make a screenshot of the map composition window of qgis. But I don't think this would be very professional. It also would cause a lot of pain :)   I'm using Qgis 1.8.0-Lisboa under Linux. The openlayers plugin is version 0.92. I am designing the layout for a touchscreen for outside use, What are some good color combination to use that will be visible under the sun light for outside use? Maybe bright neon colors? iOS app in a zombified state Live refresh shows "modified" on tagged questions even when unmodified I just want Telegram to be run and I have added it to startup apps. The point is that I need it to be minimized. Any commands? Why is orbital angular momentum not 0 when spin and linear momentum are not collinear?   Why can it be 0 when spin and linear momentum are parallel?  Like in the example of a scalar field at rest decaying into an electron and a positron via interaction $\frac{1}{2}g\phi \bar{\Psi}\Psi $   If spin is along x axis and three-momenta is along z axis, decay rate will be 0 if two spins are opposite because orbital momentum is not 0 after decaying. Print out elements from an array with a comma between elements except the last word T-SQL: How to update just date part of datetime field?