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ISI MStat 2015 PSA Problem 18 | Complex Number

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


Answer: is a pair of intersecting straight lines

ISI MStat 2015 PSA Problem 18

Precollege Mathematics

Try with Hints


Simplify the Complex. Just Solve.

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.(?)

Yes! they intersect and to get the point of intersection just use substitution . Hence it gives a pair of intersecting straight lines.

Similar Problems and Solutions



ISI MStat 2015 PSA Problem 18
Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Subscribe to Cheenta at Youtube


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


Answer: is a pair of intersecting straight lines

ISI MStat 2015 PSA Problem 18

Precollege Mathematics

Try with Hints


Simplify the Complex. Just Solve.

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.(?)

Yes! they intersect and to get the point of intersection just use substitution . Hence it gives a pair of intersecting straight lines.

Similar Problems and Solutions



ISI MStat 2015 PSA Problem 18
Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Subscribe to Cheenta at Youtube


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