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Question

Match the equation in z in ColumnI with the corresponding value of arg(z) in columnII.
ColumnI
(equation in z)
ColumnII
(principal value of arg(z))
z2z+1=02π/3
z2+z+1=0
π/3
2z2+1+i3=0π/3
2z2+1i3=0
2π/3

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Solution

(1) z2z+1=0
+1±14(1)2(1)=1±3i2tan1(yx)=tan1(π3)
=60o=π3

(2) z2+z+1=0
1±3i2tan1(31)=2π3

(3) 2z2+1+i3=0
z2=1i32tan1(3)=π3

(4) 2z2+1i3=0
z=1i32tan1(3)=2π3




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