Complex NumbersHard
Question
If z satisfies the inequality |z - 1 - 2i| ≤ 1, then
Options
A.min (arg (z)) = tan-1 (3/4)
B.max (arg(z)) = 
C.min (|z|) = √5 - 1
D.max (|z|) = √5 + 1
Solution
⇒ 
max | z | = d + r
min | z | = d - r
d = OC = √5
r = 1
θ = ⎳OCX = tan-1
α = ⎳OCA = tan-1
So principal Arg of A = θ - α = tan-1 2 - tan-1
= tan-1
max | z | = d + r
min | z | = d - r
d = OC = √5
r = 1
θ = ⎳OCX = tan-1
α = ⎳OCA = tan-1
So principal Arg of A = θ - α = tan-1 2 - tan-1
= tan-1
Create a free account to view solution
View Solution FreeMore Complex Numbers Questions
The common roots of the equations z3 + (1 + i)z + i = 0, (where i = and z1993 + 1 = 0 are - (where ω denotes the co...The locus of z which lies in shaded region is best represented by...The value of the expression + where w is an imaginary cube root of unity is-...i243 equals -...Let z, w be complex numbers such that and arg zw = π. Then arg z equals...