Find the coordinates of the point of intersection of \(\Pi\) and \(l\).
\(S\) is the point \(( 4,5 , - 5 )\). Find the shortest distance from \(S\) to \(\Pi\).
2 The complex number \(2 + \mathrm { i }\) is denoted by \(z\).
Show that \(z ^ { 2 } = 3 + 4 \mathrm { i }\).
Plot the following on the Argand diagram in the Printed Answer Booklet.
\(z\)
\(z ^ { 2 }\)
State the relationship between \(\left| z ^ { 2 } \right|\) and \(| z |\).
State the relationship between \(\arg \left( z ^ { 2 } \right)\) and \(\arg ( z )\).
3 In this question you must show detailed reasoning.
Use the formula \(\sum _ { r = 1 } ^ { n } r ^ { 2 } = \frac { 1 } { 6 } n ( n + 1 ) ( 2 n + 1 )\) to evaluate \(121 ^ { 2 } + 122 ^ { 2 } + 123 ^ { 2 } + \ldots + 300 ^ { 2 }\).