Question

Find the absolute value of each complex number.
|7 - i|

Answer 1

I know the answer is 5sqrt(2), but I don't know how they got that

Answer 2

|a+bi| = sqrt(a^2+b^2)

|7+(-1)i| = sqrt(7^2+(-1)^2)

I'll let you take it from here

Answer 3

why did you get rid of the i in sqrt(7^2+(-1)^2)?

Answer 4

You use the formula

|a+bi| = sqrt(a^2+b^2)

In the case of 7 - i, it's in the form 7+(-1)i which means a = 7 and b = -1

Answer 5

So you plug those values into the formula |a+bi| = sqrt(a^2+b^2)

Answer 6

Wait I don't understand... isn't i = sqrt(-1)?

Answer 7

yes, but with that formula, you only worry about the coefficients

Answer 8

What do you do with the i?

Answer 9

If you plot 7 - i in the complex number plane, you're basically plotting the point (7,-1) on the xy coordinate system

To find |7-i|, you're finding the distance from (0,0) to (7,-1)

Answer 10

So you can see that finding the distance from (0,0) to (7,-1) doesn't involve the term i

Answer 11

ooh

Answer 12

glad things are clicking

Answer 13

Thanks!

Answer 14

yw