We have an algebraic expression and we have to express it in the form of a complex number.
To do that we have to take into account the definition of the imaginary number i:
[tex]i=\sqrt[]{-1}[/tex]
We can now work on the expression to find the complex number it represents:
[tex]\begin{gathered} \frac{\sqrt[]{-3}}{\sqrt[]{-2}\cdot\sqrt[]{-5}} \\ \sqrt[]{-\frac{3}{(-2)(-5)}} \\ \sqrt[]{\frac{-3}{10}} \\ \sqrt[]{\frac{3\cdot(-1)_{}}{10}} \\ \sqrt[]{\frac{3}{10}}\cdot\sqrt[]{-1} \\ \sqrt[]{\frac{3}{10}}\cdot i \\ 0+\sqrt[]{\frac{3}{10}}i \end{gathered}[/tex]
Then, if we define the complex number as a + bi, then a=0 and b = √(3/10).
Answer: a=0 and b = √(3/10)
