Representations of Complex Numbers
The new functions ReIm and AbsArg make it easy to convert a complex number to either its Cartesian or polar representation.
Convert a complex number to the ordered pair
.
In[1]:=
![Click for copyable input](assets.en/representations-of-complex-numbers/In_36.png)
ReIm[3 + 4 I]
Out[1]=
![](assets.en/representations-of-complex-numbers/O_31.png)
Convert several numbers.
In[2]:=
![Click for copyable input](assets.en/representations-of-complex-numbers/In_37.png)
ReIm[{Pi, -2 I, Sqrt[-I], 3 Exp[I 2 Pi/3]}]
Out[2]=
![](assets.en/representations-of-complex-numbers/O_32.png)
Convert a complex number to the ordered pair
.
In[3]:=
![Click for copyable input](assets.en/representations-of-complex-numbers/In_38.png)
AbsArg[3 + 4 I]
Out[3]=
![](assets.en/representations-of-complex-numbers/O_33.png)
Convert several numbers.
In[4]:=
![Click for copyable input](assets.en/representations-of-complex-numbers/In_39.png)
AbsArg[{Pi, -2 I, Sqrt[-I], 3 Exp[I 2 Pi/3]}]
Out[4]=
![](assets.en/representations-of-complex-numbers/O_34.png)
Plot a complex-valued function as a curve in the complex plane.
In[5]:=
![Click for copyable input](assets.en/representations-of-complex-numbers/In_40.png)
ParametricPlot[ReIm[(-2)^x], {x, 0, 4}]
Out[5]=
![](assets.en/representations-of-complex-numbers/O_35.png)
Annotate specific points in a complex-plane plot.
In[6]:=
![Click for copyable input](assets.en/representations-of-complex-numbers/In_41.png)
JuliaSetPlot[-1, PlotRange -> 1.75,
Epilog -> {PointSize[Large], White, Point[ReIm[{I/2, -I/2, 1, -1}]]}]
Out[6]=
![](assets.en/representations-of-complex-numbers/O_36.png)