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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.

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.