Area bounded by the Complex Numbers !

Algebra Level 2

If i=√-1 and z=x+iy is any complex number on Argand Plane,

Then area described by the points z, iz and z+iz as vertices of a triangle is given by:

( x 2 + y 2 ) / 2 (x^2+y^2)/2 x 2 + y 2 x^2+y^2 x y / 2 xy/2 √ ( x 2 + y 2 ) √(x^2+y^2)

Soham Zemse by Soham Zemse , 24, India

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1 solution

This is a right angled triangle with equal legs. So the area 1/2 * leg * leg.
leg=|z|. So area= 1 2 ∗ ( x 2 + y 2 ) 2 = 1 2 ∗ ( x 2 + y 2 ) \dfrac{1}{2}*(\sqrt{x^2+y^2})^2 =\dfrac{1}{2}*(x^2+y^2)

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