ABCD is a rhombus such that its its diagonals AC and BD intersect at M and satisfy BD=2AC. If the points D and M represent the complex no. 1+i and 2-i respectively, then which complex no. does A represent?

Dear student,

BD=2 AC

D=1+i

M=2-i

Using basic mathematics and the properties of rhombus we get the coordinates of A as 3-i/2 or 1-3i/2

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The points A,B,C and D represent the numbers Z₁,Z₂,Z₃ and Z₄.ABCD is rhombus;AC=2BD.if  Z₂=2+i

,Z₄=1-2i,find Z₁ and Z₃