# Approximating exponentials in a nice to read format

I need to make some approximations, basically I have something like

$$e^{i*a} = -0.735145 + 0.67791*I$$

and I want to approximate this to something that is easily readable, like

$$e^{\frac{3*\pi}{2}*i}$$

Does mathematica have a simplify function that can do this, while I specify the form of the equation I want to end up with (like the second one)? Is there another way, besides just taking a wild guess?

Read the documentation about Rationalize

Now starting from the complex form you can build you own function

nicef = Exp[Rationalize[Im[Chop[Log[#]]], 1/16] I] &

nicef[-0.735145 + 0.67791 I]

E^((12 I)/5)


or if the input is $a$ then just Rationalize[a,1/16]

• Yes, I did try Rationalize, however my algorithm is so sensitive that not even with 0.000001 instead of 1/16, I won't get what I want. Anyway, your post does answer my question, so I will accept it. Thank you. Jan 18 '16 at 10:57