Question

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

Answer 1

Answer:

distance

Step-by-step explanation:

Usually the absolute value of a complex number is called its magnitude. The squared magnitude is the algebraic quantity that's preferable to work with.

Let

$z = a+bi$

$|z|^2 = z^* z = zz^* = |a+bi|^2= (a+bi)(a-bi) = a^2 - i^2 b^2 = a^2+b^2$

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

That's the distance from the origin to (a,b)