| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2013 |
| Session | November |
| Topic | Complex Numbers Arithmetic |
| Type | Complex conjugate properties and proofs |
| Difficulty | Easy -1.2 This is a direct proof of a fundamental property of complex conjugates requiring only substitution of z = a + bi and basic algebraic manipulation. It's a standard bookwork result that appears in most A-level/Pre-U specifications, requiring recall and straightforward verification rather than problem-solving or insight. |
| Spec | 4.02a Complex numbers: real/imaginary parts, modulus, argument4.02c Complex notation: z, z*, Re(z), Im(z), |z|, arg(z) |
7 Given that $z$ is a complex number, prove that $z z ^ { * } = | z | ^ { 2 }$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2013 Q7}}