hba 3 years ago Question...

1. hba

If $z _{1}=1-i ,z_{2}=7+i$ then the modulus of $\frac{ z _{1}-z _{2} }{ z _{1}z _{2} }$

2. hba

looks like no one is interested in helping me :D

3. hba

@ash2326 @phi

4. hba

I tried to Solve it And got the final expression as $\frac{ -6-2i }{ 8-6i }$ Do I apply the modulus now ?

5. ash2326

First find z1-z2 and z1 z2 Then take the modulus of both and divide

6. hba

@ash2326 I think you did not see my comment

7. hba

I moreover simplified it to $-3-i/4-3i$

8. ash2326

Now find modulus of -3-i and find modulus of 4-3i and divide both

9. hba

Taking a conjugate would help ?

10. hba

Well @ash2326 I tried it that way but it didn't help :(

11. ash2326

Are you getting a wrong answer?

12. niksva

multiply numerator and denominator by 4+3i it will make the problem more easier

13. hba

@ash2326 Yes

14. hba

@niksva This is what we call a conjugate and i was asking that only ?

15. ash2326

Answer is $\frac{\sqrt {10}}{5}$ What did you get?

16. niksva

@hba i know what is meant by conjugate i m telling u to rationalize the function

17. hba

$2\sqrt{2}/7$

18. hba

LoL :D

19. ash2326

You made a mistake here. Let me show $-3-i/4-3i$ $|-3-i|=\sqrt{(-3)^2+(-1)^2}=\sqrt{10}$ $|4-3i|=\sqrt{(4)^2+(-3)^2}=\sqrt {25}=5$ so you'd get $\frac{\sqrt{10}}{5}$

20. hba

Thanks A Lot @ash2326