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Q.

The descending order of the principal values of arguments of the complex numbers z1 = 1 + i, z2 = -3 + i, z3 = 1 + 3i, z4 = 1 - i is

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a

z2,z3, z1, z4

b

z4,z1, z3, z2

c

z3,z1, z2, z4

d

z3, z2, z1, z4

answer is B.

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Detailed Solution

z1=1+iArg(z1)=Tan-1 1=π4 
z2=-3+iArg(z2)=π-Tan-113=π-π6=5π6 
z3=1+i3Arg z3=Tan-1(3) =π3 
z4=1-iArg z4=Tan-1(-1)=-π4 

 Descending order z2, z3, z1, z4

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