Easy -1.2 This is a straightforward application of the modulus-argument form conversion formulas (a = r cos θ, b = r sin θ) with standard angle values. It requires only direct recall and substitution with no problem-solving or multi-step reasoning, making it easier than average even for Further Maths.
1 The complex number \(a + \mathrm { i } b\) is denoted by \(z\). Given that \(| z | = 4\) and \(\arg z = \frac { 1 } { 3 } \pi\), find \(a\) and \(b\).
Use trig to find an expression for \(a\) (or \(b\)). Obtain correct answer. Attempt to find other value. Obtain correct answer a.e.f. (Allow 3.46). State 2 equations for \(a\) and \(b\). Attempt to solve these equations. Obtain correct answers a.e.f. SR \(\pm\) scores A1 only.
OR \(b = 2\sqrt{3}\)
Answer
Marks
\(a = 2\) \(b = 2\sqrt{3}\)
Total: 4 marks
EITHER $a = 2$ | M1 A1 M1 A1 M1 M1 A1 A1 | Use trig to find an expression for $a$ (or $b$). Obtain correct answer. Attempt to find other value. Obtain correct answer a.e.f. (Allow 3.46). State 2 equations for $a$ and $b$. Attempt to solve these equations. Obtain correct answers a.e.f. SR $\pm$ scores A1 only.
OR $b = 2\sqrt{3}$
$a = 2$ $b = 2\sqrt{3}$ | | |
**Total: 4 marks**
1 The complex number $a + \mathrm { i } b$ is denoted by $z$. Given that $| z | = 4$ and $\arg z = \frac { 1 } { 3 } \pi$, find $a$ and $b$.
\hfill \mbox{\textit{OCR FP1 2007 Q1 [4]}}