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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

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

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Comment | Dear Prof Abe Thanks. Prashant |

Calculus

Answers by Expert:

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!

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