Question

1. $\frac{6div5i}{3}$
2. $\frac{-2+sqrt{-8}}{10}$

Explanation:

Problem 11: $\frac{6+5i}{3}$

Step1: Split the fraction

$\frac{6+5i}{3} = \frac{6}{3} + \frac{5i}{3}$

Step2: Simplify each term

$\frac{6}{3}=2$, so $\frac{6+5i}{3}=2+\frac{5}{3}i$

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Problem 12: $\frac{-2+\sqrt{-8}}{10}$

Step1: Simplify the imaginary square root

$\sqrt{-8}=\sqrt{4\times(-2)}=2\sqrt{2}i$

Step2: Substitute back and split fraction

$\frac{-2+2\sqrt{2}i}{10} = \frac{-2}{10} + \frac{2\sqrt{2}i}{10}$

Step3: Simplify each term

$\frac{-2}{10}=-\frac{1}{5}$, $\frac{2\sqrt{2}}{10}=\frac{\sqrt{2}}{5}$, so $\frac{-2+\sqrt{-8}}{10}=-\frac{1}{5}+\frac{\sqrt{2}}{5}i$

Answer:

1. $2+\frac{5}{3}i$
2. $-\frac{1}{5}+\frac{\sqrt{2}}{5}i$