Question

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Answer 1

Answer:

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. Hope this information will clear your doubts about this topic.

Answer 2

Answer:

- π/4 or 7π/4

Step-by-step explanation:

z = x + iy

argument @ = tan -1 (y/x)

now ...

z1 = 1 + I

@1 = tan -1 ( 1 / 1 ) = 1 = π/4

z2 = -1 + i√3

@2 = tan -1 (√3 / -1 ) = - tan -1 (√3) = - π /3

z3= -√3 - i

@3 = tan -1 (- 1 / -√3 ) = tan -1 ( 1 / √3) = π /6

z4 = √3 - i

@4 = tan -1 (- 1 / √3 ) = - tan -1 ( 1 / √3) = - π /3

z5 = i = 0 + 1i

@5 = tan^ -1 ( 1 / 0 ) = tan ^∞ = π/2

z6 = -3i = 0 - 3i

@6 = tan -1 ( -3 / 0 ) = - tan ^∞ = - π/2

z7 = 2 = 2 + 0i

@7 = tan -1 ( 0 / 2 ) = - tan ^0 = 0

z8 = -1 = - 1 + 0i

@8 = tan -1 ( 0 / -1) = - tan ^0 = 0

now ...

@1 + @2 + @3 + @4 + @5 + @6 + @7 + @8

= π/4 - π/3 + π/6 - π/3 + π/2 - π/2 + 0 + 0

hence...

@ = - π/4 or 7π/4