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complex rectangular to polar

asked 2013-10-26 00:25:45 -0500

anonymous user

Anonymous

I'm new to Sage. How do I convert a complex number like 2+3i into its polar form symbolically to get it in the form r.e^i.theta?

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answered 2013-10-26 02:43:37 -0500

tmonteil gravatar image

You can use abs() and arg() functions to compute modulus and argument of a symbolic complex number as follows:

sage: a = 2 + 3*I
sage: b = abs(a)*e^(I*(arg(a))) ; b
sqrt(13)*e^(I*arctan(3/2))
sage: bool(a == b)
True

In the other direction, you can use real_part() and imag_part()

sage: c = real_part(b) + I*imag_part(b) ; c
sqrt(13)*cos(real_part(arctan(3/2)))*e^(-imag_part(arctan(3/2))) + I*sqrt(13)*e^(-imag_part(arctan(3/2)))*sin(real_part(arctan(3/2)))
sage: c.simplify()
3*I + 2
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Asked: 2013-10-26 00:25:45 -0500

Seen: 930 times

Last updated: Oct 26 '13