The sum of principal arguments of complex numbers 1+i,-1+i root 3,- root 3- i, root 3-i, i,-3i,2, -1 is?
Answer is 11 pi/12

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Please find below the solution to the asked query:

If α is the principal argument of z=a+ib, thenIf z lies in first quadrant +,+α=tan-1baIf z lies in second quadrant -,+α=π-tan-1baIf z lies in third quadrant -,+α=tan-1ba-πIf z lies in fourth quadrant +,-α=-tan-1baz1=1+iα1=tan-11=π4z2=-1+i3α2=π-tan-13-1=tan-13=π-π3=-2π3z3=-3-iα3=tan-1-1-3-π=tan-113-π=π6-π=-5π6z4=3-iα4=-tan-1-13=-tan-113=-π6z5=i which lies on positive imaginary axis.α5=π2z6=-3i which lies on negative imaginary axis.α6=-π2z7=2 which lies on positive real axisα7=0z8=-1 which lies on negative real axisα8=πα1+α2+α3+α4+α5+α6+α7+α8=π4+2π3-5π6-π6+π2-π2+0+π=π3+8-10-2+1212=11π12 Answer

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