Answer :

Let z1 = |z1| (cos θ1 + i sin θ1) and z2 = |z2| (cos θ2 + i sin θ2)


Now, z1z2 = |z1| |z2| (cos θ1 + i sin θ1) (cos θ2 + i sin θ2)


= |z1| |z2| [cos θ1 cos θ2 + i sin θ1 cos θ2 + i cos θ1 sin θ2 + i2 sin θ1 sin θ2]


= |z1| |z2| [cos (θ1 + θ2) + i sin (θ1 + θ2)]


|z1 z2| = |z1| |z2|


And arg (z1 z2) = θ1 + θ2 = arg (z1) + arg (z2)


|z1 + z2| = |z1| + |z2| is true only when z1, z2 and O are collinear.


Also, |z1 + z2| ≥ ||z1| - |z2||

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