Question

The absolute value of any complex number a+bi is the ______ from (a,b) to (0,0) in the complex plane.

Answer 1

we know that

absolute value of a+bi

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

now, we can find distance between from (a,b) to (0,0)

$d=\sqrt{(a-0)^2+(b-0)^2}$

$d=\sqrt{a^2+b^2}$

we can see that

distance is same as absolute value

so,

The absolute value of any complex number a+bi is the distance from (a,b) to (0,0) in the complex plane.

Answer 2

The absolute value of any complex number a+bi is the Distance from (a,b) to (0,0) in the complex plane. Blank=distance.