Solve the complex analysis problem

[chwala]

The problem is attached

regards,

chwala ken

 

[susskind_leon]

Nope dude, that's incorrect. x and y are wrong. Try forming a real-valued denominator and then check again what x and y are.

 

[chwala]

i do not get it ? A complex number has a Real part and an Imaginary part. The idea is to breakdown the expression in the form x+iy so i do not understand why you are talking of real valued denominator. Kindly expound by looking at the problem and check where i went wrong.

 

[susskind_leon]

Suppose z=1/(a+i*b)
Then z not equal to 1/a + i*1/b
Why? Basic fraction calculus. You cannot "split up" a fraction among its denominator, which is what you're intending. You can split it up among the nominator though, so you should make the denominator real-valued by expanding with its complex conjugate, that is
z=(a-i*b)/((a+i*b)*(a-i*b))=(a-i*b)/(a^2+b^2)
so your final expression would be
a/(a^2+b^2)-i*b/(a^2+b^2)

If you don't understand the above, my advice would be to real a bit about basics of complex numbers on wikipedia (no offense)

 

[chwala]

Ha..,Thanks Susskind for the insight.