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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?

 

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?

Grade:11

2 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
4 years ago
223-1483_Capture.PNG
mycroft holmes
272 Points
4 years ago
From the given info, DA = ½ DM and is obtained by rotating DM by 900 in anti-clockwise direction. DM = (1+i)-(2-i) = 2i-1.
 
Hence DA = (2i-1) * i/2 = -1 – i/2.
 
Hence we get A = (2-i)+(-1-i/2) = 1 – 3i/2

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