a question in mathematic and matlab

[v9260019]

Hello everyone
If let in=input and out=output
in[1]:=(2+I)^5
out[1]:=-38+41i
then
in[2]:=%^(1/5)
out[2]:=2+i
the answer 2+i=2+i------right, but the following have some problem
in[3]:=(5+6I)^5
out[3]:=-9475-27474i
then
in[4]:=%^(1/5)
out[4]:=(-9475-27474i)^(1/5)
in[5]:=N[%]
out[5]:=7.25142-2.90118i
the answer 7.25142-2.90118i ≠ 5+6i
the above is the same in matlab , why?????????????

 

[echo47]

See equation (1):
https://mathworld.wolfram.com/ComplexExponentiation.html
In your examples "d" is zero, but the result still goes in circles. Try i^5 or just i*i*i*i*i.

 

[v9260019]

echo47
sorry
i am afraid i can't get you ,would you explain in detail-----thanks