## JenniferSmart1 Group Title How do I find absolute values of complex numbers? |7-i| one year ago one year ago

1. satellite73 Group Title

pythatgoras $|a+bi|=\sqrt{a^2+b^2}$

2. satellite73 Group Title

*pythagoras

3. satellite73 Group Title

in your case $$a=7,b=-1$$ so you can just about do it in your head

4. satellite73 Group Title

$\sqrt{7^2+1^2}=\sqrt{491}=\sqrt{50}=5\sqrt2$

5. satellite73 Group Title

not much to memorize, the hypotenuse is the square root of the sum of the squares, as in a right triangle

6. JenniferSmart1 Group Title

but what has an "i" to do with a triangle?

7. satellite73 Group Title

|dw:1358396646228:dw|

8. satellite73 Group Title

the complex numbers live in the complex plane the absolute value is the distance from the origin, which you get via pythagoras $a^2+b^2=h^2$ $h=\sqrt{a^2+b^2}$

9. JenniferSmart1 Group Title

is the triangle always in that quadrant?

10. Callisto Group Title

No, it depends on the complex number. Let a, b = +ve a+bi => quad. I -a + bi => quad. II -a - bi => quad. III a - bi => quad. IV

11. JenniferSmart1 Group Title

ahh good to know...so is "a" and "b" the length of the lines?

12. satellite73 Group Title

it doesn't make any difference however, what quadrant you are in, it is still $|a+bi|=\sqrt{a^2+b^2}$ i just put it there because your number was $$7-i$$

13. satellite73 Group Title

|dw:1358397280980:dw|

14. Callisto Group Title

|dw:1358397320522:dw|

15. JenniferSmart1 Group Title

That makes sense...I just have one more dumb question a+bi....is that the location of the point at the end of that line?

16. JenniferSmart1 Group Title

oh no that is the length of the line....durrr..sorry!!!1

17. JenniferSmart1 Group Title

the absolute value of a+bi is the length of the line...correct?

18. Callisto Group Title

a + bi a = number (coordinate) in the real part b = number (coordinate) in the imaginary part | a+bi | = length of the line => yes, I think (Actually... I haven't learnt it in the lesson yet.. So...)

19. JenniferSmart1 Group Title

that's cool...It makes sense to me though. Thanks soo much @Callisto =)

20. satellite73 Group Title

yes, it is the length of the line, that is, the distance between the complex number $$a+bi$$ and the origin