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# Calculus/Compute exponentiation of two complex numbers.

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

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

(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

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Dear Prof Abe Thanks. Prashant

Calculus

Volunteer

#### 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