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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?

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Read the documentation about Rationalize

Mathematica graphics


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]

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  • $\begingroup$ 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. $\endgroup$
    – PhysNerd90
    Jan 18 '16 at 10:57

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