Easy -1.2 This is a straightforward application of the modulus formula |z| = √(a² + b²) to find a, followed by basic arctangent calculation for the argument. It requires only direct substitution and simple algebraic manipulation with no problem-solving insight needed.
1 The complex number \(a + 5 \mathrm { i }\), where \(a\) is positive, is denoted by \(z\). Given that \(| z | = 13\), find the value of \(a\) and hence find \(\arg z\).
1 The complex number $a + 5 \mathrm { i }$, where $a$ is positive, is denoted by $z$. Given that $| z | = 13$, find the value of $a$ and hence find $\arg z$.
\hfill \mbox{\textit{OCR FP1 2012 Q1 [4]}}