Relations and Functions

Question

Find the modulus of the following complex numbers :
(2+3i)(1-i)+(3-5i)

Answer

Let             z = (2+3i)(1-i)+(3-5i) = (2 - 2i + 3i -3i²) + ( 3 -5i)
                    = (5+i) + (3-5i) = 8 -4i
$rightwards double arrow$ $space space space space space space space space space space space space space space space open vertical bar straight z close vertical bar space equals space square root of left parenthesis 8 right parenthesis squared space plus space left parenthesis negative 4 right parenthesis squared end root$
        $space space space space space space space space space space space space space space equals space space square root of 64 plus 16 end root space equals space square root of 80 space equals space 4 square root of 5$