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Question

If z1,z2 and z3,z4 are two pairs of conjugate complex numbers, then the value of arg(z1z4)+arg(z2z3) is

A
π2
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B
0
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C
π4
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D
π4
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Solution

The correct option is B 0
Given, z2=¯¯¯z1 and z4=¯¯¯z3
z1z2=|z1|2 and z3z4=|z3|2

Now, arg(z1z4)+arg(z2z3)
=arg(z1z2z4z3)
=arg(|z1|2|z3|2)
=arg(z1z32)
=arg(a), aR+
=0

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