The area (in sq. units) of the triangle whose vertices are the points represented by the complex numbers 0, z, ze^i (0

Question

The area (in sq. units) of the triangle whose vertices are the points represented by the complex numbers 0, z, ze^i (0< < ) is

Accepted Answer

Correct answer: B. (b) Let z=x+ iy Given that vertices of triangle are 0 ,z= (x+ iy ) and ze^ iα=(x+ iy)( cos + isin ) =( xcos - ysin )+i( ycos + xsin ) ∴ Area of triangle = 12(001xy1 xcosα- ysinα ycosα+ xsinα1) = 12(( xycosα+x^2 sinα)-( xycosα-y^2 sinα)) = 12( xycosα+x^2 sinα- xycosα+y^2 sinα) = 12(x^2+y^2) sin = 12 |z |^2 sinα( ∵ |z |= x^2+y^2)

$The area (in sq. units) of the triangle whose vertices are the points represented by the complex numbers 0, z, z e^{i α} (0 < α < π) is$

Solution

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