Question

Now examine |a + bi| and complete the definition below. The absolute value of any complex number a + bi is the from (a, b) to (0, 0) in the complex plane.

Answer 1

Distance

|a+bi| is the length of the vector from origin to (a,b).

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

Answer 2

Answer:

$\sqrt{a^2+b^2}$ which is the absolute value of complex plane |a+ib|

Step-by-step explanation:

The absolute value of any complex number is its modulus for which we have a formula of modulus

$\sqrt{a^2+b^2}$ where a and b are real numbers.

Please look at the attachement for complex plane of the given points (a,b) and (0,0)

The distance between two points $(x_1,y_1)$ and $(x_2,y_2)]$ will be

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here we need to find the distance between (a,b) and (0,0)

on substituting the values in distance formula we will get

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

$\Rightarrow\sqrt{a^2+b^2}$ which is the absolute value of complex plane |a+ib|