Real and imaginary complex number to the power of a complex number?

Question

Mathematics

In the task, you need to find the Real and Imaginary of the following number:
(3-i4)^(2+i)
(3-i4) translated into exponential notation, and then I don’t know how ...
I calculated in tungsten - his answer does not match the one what's in the tutorial: -3.539, -12.133

Answer 1

3-i*4 = exp(ln(5)-i*arctg(4/3)+i*2*pi*k)=exp(1.6094379-i*0.9272952+i*2*pi*k)
(3- i*4)^(2+i)=exp((1.6094379-i*0.9272952+i*2*pi*k)*(2+i))=
=exp(4.146171042-i*0.24515252+12.56637*i*k -6.283185*k)=
=(61.30217-i*15.336867)/exp(2*pi)^k
The textbook answer doesn't work for any k.