Question 48.
Find the area of the triangle formed by the points represented by z, (z+i*z) and i*z.
Answer 48.
Let z = x + iy,
then z + iz = (x + iy) + i(x + iy) = (x - y) + i(x + y)
and iz = i(x + iy) = (-y + ix)
=> vertices are (x, y), (x-y, x+y) and (-y, x)
Shifting origin to (x-y, x+y), the new vertices are
(y, - x), (0, 0) and (- x, - y)
Area of the trinagle is independent of the system of coordinates
=> reqd. area
= (1/2) modulus of determinant
l y - x l
l -x -y l
= (1/2) modulus (-y^2 - x^2)
= (1/2) (x^2 + y^2)
= (1/2)*lzl^2.
LINK to YA!
Find the area of the triangle formed by the points represented by z, (z+i*z) and i*z.
Answer 48.
Let z = x + iy,
then z + iz = (x + iy) + i(x + iy) = (x - y) + i(x + y)
and iz = i(x + iy) = (-y + ix)
=> vertices are (x, y), (x-y, x+y) and (-y, x)
Shifting origin to (x-y, x+y), the new vertices are
(y, - x), (0, 0) and (- x, - y)
Area of the trinagle is independent of the system of coordinates
=> reqd. area
= (1/2) modulus of determinant
l y - x l
l -x -y l
= (1/2) modulus (-y^2 - x^2)
= (1/2) (x^2 + y^2)
= (1/2)*lzl^2.
LINK to YA!
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