How Do You Graph the Complex Function w = z^(i+2)?

[alazhumizhu]

For example :
z={z|0<=arg z<=(pi)/6}
Draw w=z^(i+2).
I can draw w=z^2 and w=z^i
But w=z^(I+2)is a holy garbagety

 

[chiro]

Hey alazhumizhu and welcome to the forums.

You might want to consider drawing two three dimensional graphs (one for the real and one for the imaginary), or look at drawing individual "line segments" of the mapping and building up the visual intuition that way.

 

[joeblow]

$$z^k=e^{k\log z}$$

Then you can find the image by composing these easier maps.