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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

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.

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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

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.

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