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# For $z = -3 + 5i,$ evaluate $z \overline{z}.$

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I know you use the conjugate but I'm pretty confused after that

$$For z = -3 + 5i, evaluate z \overline{z}.$$

Jan 15, 2023

If $$z = a + bi$$, then $$\overline{z} = a - bi$$. So, $$z \overline{z} = (a + bi)(a-bi) = a^2 + b^2$$. Since $$(a, b) = (3, 5)$$, we have $$z \overline{z} = 3^{2} + 5^{2} = 41.$$