Question

write the following expression in the standard form a + bi. \\( zoverline{z} \\), where \\( z = 7 - 8i \\) \\( zoverline{z} = \square \\) (simplify your answer.)

Explanation:

Step1: Find conjugate of $z$

For $z=7-8i$, $\bar{z}=7+8i$

Step2: Multiply $z$ and $\bar{z}$

$$(7-8i)(7+8i)=7^2 - (8i)^2$$

Step3: Simplify the expression

$$49 - 64i^2 = 49 - 64(-1) = 49+64$$

Step4: Calculate final sum

$$49+64=113$$

Answer:

$113$ (or $113+0i$ in strict $a+bi$ form)