
complex numbers
hey i don't think this is the right thread but i couldn't find any other. can anyone help me with this question?
Find all solutions in the form z = x +iy for real x and y to the equations
i) z*3 = 2 + i
ii)iz*2 +2z = i  1
iii) exp(z) = 1 + i
cheers!!

For i) and ii) you can proceed as for ordinary algebraic equations. For iii) the solution is $\displaystyle z= \ln (1+i)$ (Wink) ...
Kind regards
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3) $\displaystyle z = \ln (1+i)$.
Taking logarithms to the base e.
Now, $\displaystyle 1+i = \sqrt{2}e^{i(\pi/4)}$ in the euler representation.
So, using this in the above equation,
$\displaystyle z = \ln (1+i)= \ln (2^{1/2}e^{i(\pi/4)})$
i.e. $\displaystyle z = \ln (2^{1/2}) +i(\pi/4)$