Question

Recall the symbol Z represents the complex conjugate of z. If z=a+bi and w=c+di show that the statement is true zw=z*w

Answer 1

z = a + bi
w = c + di

zw = (a + bi)(c + di)
zw = a(c + di) + bi(c + di)
zw = a(c) + a(di) + bi(c) + bi(di)
zw = ac + adi + bci + bdi²
zw = ac + adi + bci + bd(-1)
zw = ac + adi + bci - bd