1. ## 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!!

2. For i) and ii) you can proceed as for ordinary algebraic equations. For iii) the solution is $z= \ln (1+i)$ ...

Kind regards

$\chi$ $\sigma$

3. 3) $z = \ln (1+i)$.

Taking logarithms to the base e.

Now, $1+i = \sqrt{2}e^{i(\pi/4)}$ in the euler representation.

So, using this in the above equation,

$z = \ln (1+i)= \ln (2^{1/2}e^{i(\pi/4)})$

i.e. $z = \ln (2^{1/2}) +i(\pi/4)$