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Manipal MET2020MathematicsComplex Number

If Z₁=1+i, Z₂=-2+3 i and Z₃= a l 3 are collinear, where i^2=-1 , then the value of a will be

Options

  1. A-1
  2. B3
  3. C4
  4. D5

Correct answer

D. 5

Step-by-step solution

Given complex númbers are Z₁=(1+i) (1,1)= (a₁, b₁ )Z₂=(-2+3 i) (-2,3) (a₂, b₂ ) and Z₃= a i 3 = (0, a 3 ) (a₃, b₃ ) These three points will be collinear, if 1 2 [a₁ (b₂-b₃ )+a₂ (b₃-b₁ )+a₃ (b₁-b₂ ) ]=0 array cc & 1 (3- a 3 )-2 ( a 3 -1 )+ (1-3)=0 & 9-a 3 -2 ( a-3 3 )+0=0 & 9-a-2 a+6=0 & 3 a=15 & a=5 array

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