Pre-U Pre-U 9794/1 2013 November — Question 7

Exam BoardPre-U
ModulePre-U 9794/1 (Pre-U Mathematics Paper 1)
Year2013
SessionNovember
TopicComplex Numbers Arithmetic
TypeComplex conjugate properties and proofs
DifficultyEasy -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.
Spec4.02a 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 \(z z ^ { * } = | z | ^ { 2 }\).

7 Given that $z$ is a complex number, prove that $z z ^ { * } = | z | ^ { 2 }$.

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