Given z1+i‌z2=0 ⇒‌‌z1=(−i)z2 Taking argument on both sides, we get arg(z1)=arg{(−i)⋅z2} ⇒‌‌arg(z1)=arg(−i)+arg(z2)  (by property)
⇒arg(z1)−arg(z2)=tan−1(‌
−1
0
)=−‌
Ï€
2
⇒arg(z1)+arg(z2)=‌
−π
2
....(i) [∵arg(z)=−arg(z)] and ‌‌arg(z1z2)=‌
Ï€
3
⇒‌‌arg(z1)+arg(z2)=‌
Ï€
3
⇒‌‌−arg(z1)+arg(z2)=‌
Ï€
3
.......(ii) On adding Eqs. (i) and (ii), we get 2‌arg(z2)=‌