What is the absolute value of the number (1+i)(1+2i)(1+3i)?

We'll multiply the first two
factors:

(1+i)*(1+2i) = 1 + i + 2i +
2i^2

Since i^2 = -1, we'll
have:

(1+i)*(1+2i) = 1 + 3i -
2

(1+i)*(1+2i) = -1 + 3i

Now,
we'll multiply both sides by (-1+3i):

(1+i)*(1+2i)*(1+3i) =
(-1 + 3i)*(1 + 3i)

(1+i)*(1+2i)*(1+3i) = (3i)^2 -
1^2

(1+i)*(1+2i)*(1+3i) = -9 - 1 =
-10

The absolute value of the number
(1+i)*(1+2i)*(1+3i) = |-10| = 10.