Prove that two straight lines with complex slopes μ_1 and μ_2 are parallel and perpendicular according as μ_1 = μ_2 and μ_1 + μ_2 = 0. Hence if the straight lines α^� z + αz^� + c = 0 and β^� z + βz^� + k = 0 are parallel and perpendicular according as α^� β − αβ^� = 0 and α^� β + αβ^� = 0.


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Question Number 19505 by Tinkutara last updated on 12/Aug/17

$Prove that two straight lines with$ $complex slopes μ_{1} and μ_{2} are parallel$ $and perpendicular according as μ_{1} = μ_{2}$ $and μ_{1} + μ_{2} = 0 . Hence if the straight$ $lines \bar{α} z + α \bar{z} + c = 0 and \bar{β} z + β \bar{z} + k = 0$ $are parallel and perpendicular according$ $as \bar{α} β - α \bar{β} = 0 and \bar{α} β + α \bar{β} = 0 .$
	Answered by ajfour last updated on 12/Aug/17

	$complex slope μ_{1} = - \frac{α}{\bar{α}}$ $μ_{2} = - \frac{β}{\bar{β}}$ $so μ_{1} = μ_{2} \Rightarrow α \bar{β} - \bar{α} β = 0$ $and μ_{1} + μ_{2} = 0 \Rightarrow α \bar{β} + \bar{α} β = 0 .$
	Commented by Tinkutara last updated on 12/Aug/17

	$Thank you very much Sir!$
	Commented by ajfour last updated on 12/Aug/17

	$it is a matter of complex slopes . .$
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