Write the argumen

As we know that,

arg (z1z2) = arg(z1)+arg(z2) so,

arg (z1z2z3) = arg(z1)+arg(z2)+arg(z3)

arg((1+√3 i)(1+i)(cos θ+ i sin θ)

= arg(1+√3 i)+arg(1+i)+arg(cos θ + i sin θ).......... (1)

arg(z1 ) = θ

z2 = arg(1+i)

z3 = arg(cos θ + i sin θ)

1(cos θ + i sin θ)

arg(z3 ) = θ

In r(cos θ + i sin θ) , arg(z) = θ

By putting the value of all arg in 1, we get

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