Question

Complex numbers: given z1=1-i, z2=-2+4i, z3=(square root 3)-2i, evaluate: Re(conjugate of z1 + z2) and Im(z1-z2)...

Answer 1

\[z_1=1-i\\
z_2=-2+4i\\
z_3=\sqrt3-2i\]
If \(\overline{z}\) is the conjugate of \(z\), then
\[\begin{align*}\overline{z_1+z_2}&=\overline{(1-i)+(-2+4i)}\\
&=\overline{-1+3i}\\
&=-1-3i
\end{align*}\]
So, what's the real part of that?
\(\Re(\overline{z_1+z_2})=\cdots\)

Answer 2

Finding \(\Im(z_1-z_2)\) is pretty easy, too. But I'm wondering why \(z_3\) was provided if it's not used at all?