This is a beautiful problem from ISI MSTAT 2015 PSA problem 18 based on complex number. We provide sequential hints so that you can try.
The set of complex numbers $z$ satisfying the equation \( (3+7 i) z+(10-2 i) \bar{z}+100=0\) represents, in the complex plane
Complex number representation
Straight line
But try the problem first...
Answer: is a pair of intersecting straight lines
ISI MStat 2015 PSA Problem 18
Precollege Mathematics
First hint
Simplify the Complex. Just Solve.
Second Hint
Let \(z = x+iy, \bar{z} = x-iy\) Then the given equation reduces to \((13x-9y+100)+i(5x-7y) = 0\).
Which implies \(13x-9y+100 = 0, 5x-7y = 0\).
They do intersect.(?)
Final Step
Yes! they intersect and to get the point of intersection just use substitution . Hence it gives a pair of intersecting straight lines.
This is a beautiful problem from ISI MSTAT 2015 PSA problem 18 based on complex number. We provide sequential hints so that you can try.
The set of complex numbers $z$ satisfying the equation \( (3+7 i) z+(10-2 i) \bar{z}+100=0\) represents, in the complex plane
Complex number representation
Straight line
But try the problem first...
Answer: is a pair of intersecting straight lines
ISI MStat 2015 PSA Problem 18
Precollege Mathematics
First hint
Simplify the Complex. Just Solve.
Second Hint
Let \(z = x+iy, \bar{z} = x-iy\) Then the given equation reduces to \((13x-9y+100)+i(5x-7y) = 0\).
Which implies \(13x-9y+100 = 0, 5x-7y = 0\).
They do intersect.(?)
Final Step
Yes! they intersect and to get the point of intersection just use substitution . Hence it gives a pair of intersecting straight lines.
