If z1, z2 and z3, z4 are 2 pairs of complex conjugate numbers, then arg ((z1/z4))+ arg ((z2/z3)) equals :

Question

If z1, z2 and z3, z4 are 2 pairs of complex conjugate numbers, then arg ((z1/z4))+ arg ((z2/z3)) equals : (A) 0 (B) (π/2) (C) (3π/2) (D) π

Tardigrade Admin · Accepted Answer

Z2 = barZ1 Z4 = barZ3 arg ((Z1/Z4)) + arg ((Z2/Z3)) = arg Z1 - arg Z4 + arg Z2 - arg Z3 = arg Z1 - arg barZ3 + arg barZ1 - arg Z3 = arg Z1 + arg Z3 - arg Z1 - arg Z3 = 0

Q. If $z_{1}, z_{2}$ and $z_{3}, z_{4}$ are 2 pairs of complex conjugate numbers, then arg $(\frac{z _{1}}{z _{4}}) + a r g (\frac{z _{2}}{z _{3}})$ equals :

0

$\frac{π}{2}$

$\frac{3 π}{2}$

$π$

Q. If z1​,z2​ and z3​,z4​ are 2 pairs of complex conjugate numbers, then arg (z4​z1​​)+arg(z3​z2​​) equals :

0

2π​

23π​

π

Z2​=Z1​ˉ​&Z4​=Z3​ˉ​ arg(Z4​Z1​​)+arg(Z3​Z2​​) =argZ1​−argZ4​+argZ2​−argZ3​ =argZ1​−argZˉ3​+argZˉ1​−argZ3​ =argZ1​+argZ3​−argZ1​−argZ3​=0

Q. If $z_{1}, z_{2}$ and $z_{3}, z_{4}$ are 2 pairs of complex conjugate numbers, then arg $(\frac{z _{1}}{z _{4}}) + a r g (\frac{z _{2}}{z _{3}})$ equals :

$\frac{π}{2}$

$\frac{3 π}{2}$

$π$