Question

simplify the expression and write the result in standard form, ( a + bi ). write all numbers as integers or simplified fractions. (\frac{-26 + sqrt{-180}}{12} = square)

Explanation:

Step1: Simplify the square root

$\sqrt{-180} = \sqrt{36 \times (-5)} = 6\sqrt{5}i$

Step2: Split the fraction

$\frac{-26 + 6\sqrt{5}i}{12} = \frac{-26}{12} + \frac{6\sqrt{5}i}{12}$

Step3: Simplify each term

$\frac{-26}{12} = -\frac{13}{6}$, $\frac{6\sqrt{5}i}{12} = \frac{\sqrt{5}}{2}i$ (or $\frac{3\sqrt{5}}{6}i$)

Answer:

$-\frac{13}{6} + \frac{3\sqrt{5}}{6}i$