How to solve absolute value of complex numbers?

Question

How do you solve:
|w*z|
w=1+4i, z=2-7i

Answer 1

|w*z|
w=1+4i, z=2-7i
|w*z| =| (1+4i)(2-7i)| = | 30 + i| = sqrt( 30^2 +1) .

Answer 2

w * z = (1+4i) *(2-7i) = 2 -7i +4i -28 i^2 = 2 - 3i +28
(using i^2 = -1)
= 30 - 3i

now, absolute value of w*z = [(30)^2 + (3)^2 ] ^ .5
= 30.14962686
(using absolute value of complex no. a+ib is square root of (a^2 + b^2). )

Answer 3

It is called the mondulus.

|a+ib|=(a^2+b^2)^(1/2)