Prove-that-two-straight-lines-with-complex-slopes-1-and-2-are-parallel-and-perpendicular-according-as-1-2-and-1-2-0-Hence-if-the-straight-lines-z-z-c-0-and-z

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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