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Calculus/Compute exponentiation of two complex numbers.

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Question
Dear Prof Abe

Can we compute exponentiation of two complex numbers?

Example - 1+2i and 2+3i

I.e 1+2i raised to power of 2+3i

Thanks
Prashant

Answer
Yes, check these links:
http://www.cut-the-knot.org/do_you_know/complex.shtml
http://mathforum.org/library/drmath/view/52251.html
http://math.stackexchange.com/questions/689846/raising-a-complex-number-to-integ
http://mathworld.wolfram.com/ComplexExponentiation.html

In your case,
(1+2i)^(2+3i) = 5*exp(-3*arctan(2))*(cos((3/2)*ln(5)+2*arctan(2))+i*sin((3/2)*ln(5)+2*arctan(2)))
or approximately  -0.01513267246-.1798674838*i

Calculus

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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