Maths Help?

Question

Find the numerical values for a and b from

a + ib = [ (3 + i) / (5+i) ] ^5

THANKYOU FOR ANY HELP

Answer 1

Given a + ib = [ (3 + i) / (5 + i) ] ^5
Solve for a and b.

[ (3 + i) / (5 + i) ] ^5

Multiply numerator and denominator by the complex conjugate.

[ (3 + i) / (5 + i) ] ^5
= [ (3 + i)(5 - i) / {(5 + i)(5 - i) ] ^5
= [ (16 + 2i) / 26 ] ^5
= [ (8 + i) / 13 ] ^5
= (27,688 + 15,361 i) / 371,293

a = 27,688 / 371,293
b = 19,841 / 371,293

Answer 2

Treat i as if it was an unknown constant ; like x.
Then eliminate the i from the denominator:
(3+i)(5-i)/(26) =(8+i/13)
then solve
[ (3 + i) / (5+i) ] ^5 = (27588 +19841 i) / 371293
a = 27588/371293
b =19841 / 371293