Question

Me pueden ayudar con los siguientes problemas de álgebra por favor​

Answer 1

1)

$2\sqrt{-4}+\frac{1}{3}\sqrt{-36}-\sqrt[3]{-64}  \\\\Nota: i=\sqrt{-1}\\\\Entonces: \sqrt{-4}=\sqrt{-1}  \sqrt{4}=i\sqrt{4}  \\\\2(i\sqrt{4} )+\frac{1}{3}(i\sqrt{36} )- (-\sqrt[3]{64} )=\\\\2(2i)+\frac{1}{3}(6i)-(-4) =\\\\4i+2i+4=\\\\4+6i$

2)

$(-5+3i)-(-1+4i)=\\\\(-5+3i)+(1-4i)=\\\\-4-i$

3)

$(-2-i)(4-3i)=\\\\-8+3i^{2} +6i-4i=\\\\-8-3+2i=\\\\-11+2i$

4)

$\frac{2+i}{1-3i}=  (\frac{2+i}{1-3i})(\frac{1+3i}{1+3i} )=\\\\\frac{2+3i^{2} +6i+i}{1-9i^{2}+3i-3i } =\\\\\frac{2-3+7i}{1+9}=\frac{-1+7i}{10}=\frac{-1}{10} +\frac{7i}{10}$

5)

$(-1+i)(-1+i)=1+i^{2} -i-i=1-1-2i=-2i$