Question

If z complex number prove (z1+z2)*=z1*+z2*

Answer 1

does \(z^*\) mean \(\overline z\) ?

Answer 2

Let \(z_1=(a_1,b_1)\) and \(z_2=(a_2,b_2)\). Then \({z_1}^*=(a_1,-b_1)\) and \({z_2}^*=(a_2,-b_2)\).

Clearly, \(z_1+z_2=(a_1+a_2,b_1+b_2)\), so \((z_1+z_2)^*=(a_1+a_2,-b_1-b_2)\), which is the same as \({z_1}^*+{z_2}^*\).