Most Important Selected Qs for JEE AdvancedMathematicsComplex Number

If the complex numbers z₁, z₂, z₃ & z₄ taken in that order are the vertices of a rhombus, then -

Options

AZ ₁+ z ₃= z ₂+ z ₄
B|z₁-z₂ |= |z₂-z₃ |
Cz ₁- Z ₃ z ₂- Z ₄ is purely imaginary
D|z₃-z₁ |= |z₄-z₂ |

Correct answer

C. z ₁- Z ₃ z ₂- Z ₄ is purely imaginary

Step-by-step solution

As it is a rhombus |z₁-z₂ |= |z₂-z₃ | & z ₁+ z ₃= z ₂+ z ₄ Diagonals of rhombus are perpendicular bisectors z₁-z₃ z₂-z₄ = 2 z₁-z₃ z₂-z₄ is purely imaginary.

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