Complex Numbers And Quadratic Equations

Question
CBSEENMA11015657

Let z, w be complex numbers such that z iw + = 0 and arg zw = π. Then arg z equals

  • π/4

  • 5π/4

  • 3π/4

  • π/2

Solution

C.

3π/4

Since z + iw = 0 ⇒ z = −iw
⇒ z = iw
⇒ w = -iz
Also arg(zw) = π
⇒ arg (-iz2) = π
⇒ arg (-i) + 2 arg(z) = π
negative straight pi over 2 space plus space 2 arg space left parenthesis straight z right parenthesis space equals space straight pi space space left parenthesis because space arg space left parenthesis negative straight i right parenthesis space equals space minus straight pi divided by 2 right parenthesis
2 space arg space left parenthesis straight z right parenthesis space equals space fraction numerator 3 straight pi over denominator 2 end fraction
arg space left parenthesis straight z right parenthesis space equals space fraction numerator 3 straight pi over denominator 4 end fraction

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