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MAT334--Misc / Class Participation
« on: October 08, 2018, 04:30:27 PM »
How is the Class and Tutorial participation calculated for the bonus component of the final grade?
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MAT334--Lectures & Home Assignments / Section 1.2 Question 18
« on: September 23, 2018, 05:19:33 PM »
I'm struggling with this question, and I was hoping someone could help me out: $\renewcommand{\Re}{\operatorname{Re}} \renewcommand{\Im}{\operatorname{Im}}$
Show that two lines $\Re(a+ib)=0$ and $\Re(c+id)=0$ are perpendicular $ \iff \Re(a \bar{c}) = 0$
From section 1.2: Let $a = A+iB$ and $c= C+iD$. Then the lines are $Ax-By+\Re(b)=0$ and $Cx-Dy+\Re(d)=0$
Setting the slope of the first equal to the negative reciprocal of the other I get: $\frac{A}{B} = - \frac{D}{C} \iff AC=-BD$
Finally, $\Re(a \bar{c}) = AC-BD= 2AC$
How do I proceed?
Thanks!
Show that two lines $\Re(a+ib)=0$ and $\Re(c+id)=0$ are perpendicular $ \iff \Re(a \bar{c}) = 0$
From section 1.2: Let $a = A+iB$ and $c= C+iD$. Then the lines are $Ax-By+\Re(b)=0$ and $Cx-Dy+\Re(d)=0$
Setting the slope of the first equal to the negative reciprocal of the other I get: $\frac{A}{B} = - \frac{D}{C} \iff AC=-BD$
Finally, $\Re(a \bar{c}) = AC-BD= 2AC$
How do I proceed?
Thanks!
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