ABCD is a rhombus. its diagonals AC and BD intersect at the point M and satisfy BD=2AC. if the points D and M represent complex nos. 1+i and 2-i resp. then find out the complex no. represented by A.

From figure D(1,1) and M(2,-1)

M is mid point of DM and AC

also AC is perpendicular to Db , and given DB =2AC

so from figure B(3 - 3i)

and DM = (5)^1/2  so AM shld be 2.(5)^1/2 units

slope od DB is -2 ; so slope of AC is 1/2

so C (-2 -3i) and A (6 + i)

Hence solved

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