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AP EAMCET202017 Sep 2020Evening ShiftMathematicsComplex NumberActual

Let (z₁, z₂ ) be two complex numbers such that ( z ₁-i z ₂=0 ) and ( (z₁ z₂ )= 3 4 ), then ( (z₁ )= )

Options

  1. A( 4 )
  2. B( - 8 )
  3. C( 8 )
  4. D( 3 )

Correct answer

C. ( 8 )

Step-by-step solution

Given ( z ₁-i z ₂=0 ) ( array ll & z ₁=i z ₂ & z ₁= i z₂ & z₁=-i z₂ array ) Clearly argument of (z₁= ) argument of (z₂- 2 ) or argument (z₁= ) argument (z₂- 2 ) ( ) argument (z₂= argument z₁+ 2 ) Let argument (z₁= ) Then, given argument ( (z₁ z₂ )= 3 4 ) ( ) argument (z₁+ argument z₂= 3 4 ) ( aligned + + 2 & = 3 4 2 & = 3 4 - 2 = 8 aligned )

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