202109151516 CYU 7.1

If $a=3+4i$ , what is the product $a^*a$ ?

Background. (Complex conjugate)

The complex conjugate of $a+bi$ is equal to $a-bi$ .

$\begin{aligned} a^*a & = (3-4i)(3+4i) \\ & = (3)(3)+(3)(4i)+(-4i)(3)+(-4i)(4i) \\ & = 9 - 16i^2 \\ & = 9 - 16(-1)\\ & = 9+16 \\ & = 25 \\ \end{aligned}$

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