Complex Numbers 4 Question 6

6. The complex numbers z1,z2 and z3 satisfying z1z3z2z3=1i32 are the vertices of a triangle which is

(a) of area zero

(b) right angled isosceles

(c) equilateral

(d) obtuse angled isosceles

Objective Questions II

(One or more than one correct option)

Show Answer

Answer:

Correct Answer: 6. (c)

Solution:

  1. z1z3z2z3=1i32=(1i3)(1+i3)2(1+i3)

=1i232(1+i3)

=42(1+i3)

=2(1+i3)

z2z3z1z3=1+i32=cosπ3+isinπ3

z2z3z1z3=1 and argz2z3z1z3=π3

Hence, the triangle is an equilateral.

Alternate Solution

z1z3z2z3=1i32z2z3z1z3=21i3=1+i32=cosπ3+isinπ3argz2z3z1z3=π3 and also |z2z3z1z3|=1

Therefore, triangle is equilateral.



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