# meaning of $z^*$ (Complex number)

Solve the equation $z+2z^*=\frac{15}{2+i}$.

I want to ask what's the meaning of $z^*$?

I think it means $\bar z$ the complex conjugate of z

• What is $z$ here? – Mathxx Oct 18 '15 at 17:18
• You are asked to find it, it's like solving and equation for x, but now z is a complex number ie $z = a + ib$ so $z^* = a - ib$ – Noctisdark Oct 18 '15 at 17:20
• ;), if you don't need anymore assistant you can mark this answered ! – Noctisdark Oct 18 '15 at 17:22

Write $z=x+iy$ then $z^•=x-iy$ and $z+2z^*=3x-iy$ and our equation looks like

$$3x-iy={15\over 5}(2-i)=6-3i$$

and so $z=2+3i$

• Um, $z+z^*=2x$, not $2x-iy$. The $iy$s cancel. – Akiva Weinberger Oct 18 '15 at 17:45
• I edit thanks @Akiva Weinberger – marwalix Oct 18 '15 at 18:33
• Then $z+2z^*=(x+iy)+(2x-2iy)=3x-iy$. – Akiva Weinberger Oct 18 '15 at 23:41