simplify the abselute value

Question

I3+5iI

Answer 1

To simplify the expression, we first need to determine the absolute value of a complex number.

The absolute value of a complex number z, denoted as |z|, is given by:
|z| = sqrt((Re(z))^2 + (Im(z))^2)

In this case, we have I3+5iI. Let's break it down:

Re(I3+5iI) = Re(3i + 5i^2) = Re(3i - 5) = -5

Im(I3+5iI) = Im(3i + 5i^2) = Im(3i - 5) = 3

So, we have:
|I3+5iI| = sqrt((-5)^2 + 3^2) = sqrt(25 + 9) = sqrt(34)

Therefore, the simplified absolute value of I3+5iI is sqrt(34).