Question

If z1 and z2 are complex numbers then prove that arg(z1/z2) = arg(z1) - arg(z2)

Answer 1

Step-by-step explanation:

Given :-

• |z1 + z2| = |z1| + |z2|

To Find :-

• prove that arg(z1/z2) = arg(z1) - arg(z2)

Solution :-

On squaring both sides

=> |z1|2 + |z2|2 + 2|z1| |z2|

Because(arg z1 – arg z2) = |z1|2 + |z2|2 + 2|z1| |z2|

=> 2|z1| |z2|

Because (arg z1 – arg z2) = 2|z1| |z2|

=> (arg z1 – arg z2) = 1

=> arg (z1) – arg (z2) = 0.

Hence proved arg(z1) = arg(z2)

more information :-

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