the points abc and d represent the numbers z1z2z3, Mathematics

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the points abc and d represent the numbers z1z2z3

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

Ans) POI of diagonals: (3-i)/2.

Using concept of rotation:

2(0.5+2i)/2z1 + i-3 = i/2

Solving for Z1

Z1 = -1.5i +5.5

Now, using midpoint formula to get Z3

Z3 + Z1 = 2(3-i)/2

Z3=0.5i-2.5

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