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Complex numbers z1, z2, z3 are the vertices A, B, C respectively of an isosceles right angled
triangle with right angle at C. Show that (z1 – z2)2 = 2(z1 – z3)(z3 – z2).

Asked by gargpuneet989 15th August 2018, 7:16 AM
Answered by Expert
Answer:
begin mathsize 16px style Applying space rotation space about space point space straight C
fraction numerator straight z subscript 2 minus straight z subscript 3 over denominator straight z subscript 1 minus straight z subscript 3 end fraction equals straight e to the power of straight i straight pi over 2 end exponent............. left parenthesis straight i right parenthesis
Applying space rotation space about space point space straight B
fraction numerator straight z subscript 1 minus straight z subscript 2 over denominator straight z subscript 3 minus straight z subscript 2 end fraction equals square root of 2 straight e to the power of straight i straight pi over 4 end exponent......... left parenthesis ii right parenthesis
Applying space rotation space about space point space straight A
fraction numerator straight z subscript 2 minus straight z subscript 1 over denominator straight z subscript 3 minus straight z subscript 1 end fraction equals square root of 2 straight e to the power of negative straight i straight pi over 4 end exponent
Multiplying space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis
fraction numerator open parentheses straight z subscript 1 minus straight z subscript 2 close parentheses open parentheses straight z subscript 2 minus straight z subscript 1 close parentheses over denominator open parentheses straight z subscript 3 minus straight z subscript 2 close parentheses open parentheses straight z subscript 3 minus straight z subscript 1 close parentheses end fraction equals 2
Solving space further space you space will space get space required space result.
end style
Answered by Expert 27th August 2018, 12:09 PM
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