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Question

If for complex numbers z1 and z2,arg(z1)arg(z2)=0, then |z1z2| is equal to

A
|z1|+|z2|
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B
|z1||z2|
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C
||z1||z2||
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D
0
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Solution

The correct option is C ||z1||z2||
Let
z1=r1(cosθ+isinθ)=r1eiθ
z2=r2(cosθ+isinθ)=r2eiθ
z1z2=(r1r2)(eiθ)
|z1z2|=|r1r2|
Now r1=|z1| and r2=|z2|
|z1z2|=||z1||z2||

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