What is 2/3+1/6 sqrt(-45) ?

The solution to 2/3+1/6 sqrt(-45) is 2/3+(sqrt(5))/2 i

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simplify 2/3+1/6 sqrt(-45)

simplify

\frac{2}{3} + \frac{1}{6} - 45

\frac{2}{3} + \frac{5}{2} i

Solution steps

\frac{2}{3} + \frac{1}{6} - 45

- 45 = 35 i

= \frac{2}{3} + \frac{1}{6} \cdot 35 i

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

\frac{1}{6} \cdot 35 i = \frac{1 \cdot 3 5}{6} i

= \frac{2}{3} + \frac{1 \cdot 3 5}{6} i

Apply rule:

1 \cdot a = a

\frac{1 \cdot 3 5}{6} i = \frac{3 5}{6} i

= \frac{2}{3} + \frac{3 5}{6} i

Cancel

\frac{3 5}{6} : \frac{5}{2}

= \frac{2}{3} + \frac{5}{2} i

\frac{25 x y}{125 x y ^{8}}

\frac{5}{6} \times \frac{1}{5} \times 3

9 \frac{1}{8} + 9 \frac{1}{8}

\frac{1}{7 - 3}

\frac{2 + 2 i}{2}

What is 2/3+1/6 sqrt(-45) ?
The solution to 2/3+1/6 sqrt(-45) is 2/3+(sqrt(5))/2 i