Most Important Selected Qs for JEE AdvancedMathematicsComplex Number
For the equation (2+3 i) z+(2-3 i) z -6=0 , which of the following is true -
Options
- AThe complex number with minimum modulus satisfying the given equation is 6 13 - 9 13 i .
- BThe argument of any complex number satisfying the given equation is ⁻¹ 2 3 .
- CAny z satisfying the given equation also satisfies z=(3+i)+ (3+2 i) for suitable R .
- DIf z₁ & z₂ are the two points satisfying given equation such that Re (z₁ )=0 & Im (z₂ )=0 , then 1 2 |z₁ | |z₂
Correct answer
D. If z₁ & z₂ are the two points satisfying given equation such that Re (z₁ )=0 & Im (z₂ )=0 , then 1 2 |z₁ | |z₂
Step-by-step solution
Put z=x+i y(2+3 i)(x+i y)+(2-3 i)(x-i y)-6=02(2 x-3 y)-6=02 x-3 y=3 Option A : In figure P represents the complex number with minimum modulus. Equation of OP is y=- 3 2 x Solving OP with AB , we get 6 13 - 9 13 i. Option B is incorrect. Option C : z-(3+i) 3+2 i is purely real z-(3+i) 3+2 i = z -(3-i) 3-2 i only solving it gives same line. Option D : 1 2 |z₁ | |z₂ |= 1 2 3 2 = 3 4 .