If the points represented by the complex number z1=a+ib, z2=a'+ib' and z1 -z2 are collinear, then

Question

If the points represented by the complex number z1=a+ib, z2=a'+ib' and z1 -z2 are collinear, then (A) ab' + a'b = 0 (B) ab' - a'b = 0 (C) ab + a'b' = 0 (D) ab - a'b' = 0

Tardigrade Admin · Accepted Answer

By the given condition |a&b&1 a'&b'&1 a-a'&b-b'&1|=0 Operate R3 - R1 + R2, we get |a&b&1 a'&b'&1 0&0&1|=0 ⇒ ab'-a'b=0

Q. If the points represented by the complex number $z_{1} = a + ib, z_{2} = a^{'} + i b^{'}$ and $z_{1} - z_{2}$ are collinear, then

ab' + a'b = 0

ab' - a'b = 0

ab + a'b' = 0

ab - a'b' = 0

By the given condition

$∣ ∣ a a^{'} a - a^{'} b b^{'} b - b^{'} 111 ∣ ∣ = 0$

Operate $R_{3} - R_{1} + R_{2}$ , we get

$∣ ∣ a a^{'} 0 b b^{'} 0 111 ∣ ∣ = 0$

$\Rightarrow a b^{'} - a^{'} b = 0$

Q. If the points represented by the complex number z1​=a+ib,z2​=a′+ib′ and z1​−z2​ are collinear, then