Q.

If the complex numbers iz, z and z+ iz represent the three vertices of a triangle, then the area of the triangle is

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a

1

b

12z2

c

12

d

12z+iz2

answer is B.

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Detailed Solution

Given z,iz and z+iz be the vertices of a triangle , thenlet z=x+iy∴ iz=-y+ix,z+iz=x-y+ix+yHence , required area =12xy1-yx1x-yx+y1                                   =12xy1-yx100-1R3→R3-R1+R2                                   =-12x2+y2                                   =12z2
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If the complex numbers iz, z and z+ iz represent the three vertices of a triangle, then the area of the triangle is