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.

Complex Number – ISI MStat Year 2015 PSA Question 18


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

  • a straight line
  • a pair of intersecting straight lines
  • a point
  • a pair of distinct parallel straight lines

Key Concepts


Complex number representation

Straight line

Check the Answer


But try the problem first…

Answer: is a pair of intersecting straight lines

Source
Suggested Reading

ISI MStat 2015 PSA Problem 18

Precollege Mathematics

Try with Hints


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.

ISI MStat 2015 PSA Problem 18
Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

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