8 In this question you must show detailed reasoning.
Express \(( 6 + 5 \mathrm { i } ) ( 7 + 5 \mathrm { i } )\) in the form \(a + b \mathrm { i }\).
You are given that \(17 ^ { 2 } + 65 ^ { 2 } = 4514\). Using the result in part (i) and by considering (6-5i)(7-5i) express 4514 as a product of its prime factors.