Moderate -0.8 This is a straightforward application of complex number multiplication and division using standard algebraic techniques. While it requires careful arithmetic (multiplying out brackets, rationalizing the denominator), it involves only direct recall of basic complex number operations with no problem-solving or conceptual insight needed. Being from FP1, it's testing foundational further maths skills, but remains a routine textbook exercise.
1 Two complex numbers are given by \(\alpha = - 3 + \mathrm { j }\) and \(\beta = 5 - 2 \mathrm { j }\).
Find \(\alpha \beta\) and \(\frac { \alpha } { \beta }\), giving your answers in the form \(a + b \mathrm { j }\), showing your working.
1 Two complex numbers are given by $\alpha = - 3 + \mathrm { j }$ and $\beta = 5 - 2 \mathrm { j }$.\\
Find $\alpha \beta$ and $\frac { \alpha } { \beta }$, giving your answers in the form $a + b \mathrm { j }$, showing your working.
\hfill \mbox{\textit{OCR MEI FP1 2010 Q1 [5]}}