Q.

If z1, z2 and z3, z4 are two pairs of conjugate complex numbers, then arg⁡z1z4+arg⁡z2z3 equal

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a

0, π

b

π, –π

c

π2,3π2

d

0,2π

answer is D.

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Detailed Solution

arg⁡z1z4+arg⁡z2z3   =arg⁡z1z2z4z3+2kπ=arg⁡z12z32+2kπ=2kπwhere k = 0 or 1  [ z1= z3 = i, gives answer 2p and z1 = z3 = 1, gives answer 0]
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If z1, z2 and z3, z4 are two pairs of conjugate complex numbers, then arg⁡z1z4+arg⁡z2z3 equal