Let `Z_(1)=x_(1)+iy_(1)`, `Z_(2)=x_(2)+iy_(2)` be complex numbers in fourth quadrant of argand plane and `|Z_(1)|=|Z_(2)|=1`, `Ref(Z_(1)Z_(2))=0`. The

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Let `Z_(1)=x_(1)+iy_(1)`, `Z_(2)=x_(2)+iy_(2)` be complex numbers in fourth quadrant of argand plane and `|Z_(1)|=|Z_(2)|=1`, `Ref(Z_(1)Z_(2))=0`. The

Let `Z_(1)=x_(1)+iy_(1)`, `Z_(2)=x_(2)+iy_(2)` be complex numbers in fourth quadrant of argand plane and `|Z_(1)|=|Z_(2)|=1`, `Ref(Z_(1)Z_(2))=0`. The complex numbers `Z_(3)=x_(1)+ix_(2)`, `Z_(4)=y_(1)+iy_(2)`, `Z_(5)=x_(1)+iy_(2)`, `Z_(6)=x_(6)+iy`, will always satisfy
A. `|Z_(4)|=1`
B. `arg(Z_(1)Z_(4))=-pi//2`
C. `(Z_(5))/(cos(argZ_(1)))+(Z_(6))/(sin(argZ_(1)))` is purely real
D. `Z_(5)^(2)+(barZ_(6))^(2)` is purely imaginergy

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A::B::C::D
`(a,b,c,d)` `Z_(1)=e^(itheta_(1))`, `Z_(2)=e^(itheta_(2))`, `Re(Z_(1)Z_(2))=0impliestheta_(1)+theta_(2)=-pi//2`, (as `z_(1)`, `z_(2)` lie in fourth quadrant)
`Z_(3)=e^(-itheta_(1))`, `Z_(4)=-e^(itheta_(1))`, `Z_(5)=costheta_(1)(1-i)`, `Z_(6)=sintheta_(1)(-1+i)`

4 views Answered 2023-02-05 15:29