Respuesta :

DeanR

I think the question is simplify

[tex]\dfrac{\sqrt{-16}}{3 - 3i} + 1-2i[/tex]

[tex]= \dfrac{4\sqrt{-1}}{3(1-i)}+ 1-2i[/tex]

[tex]= \dfrac{4}{3}\dfrac{i}{1-i} \cdot \dfrac{1+i}{1+i} + 1-2i[/tex]


[tex]= \dfrac{4}{3} \dfrac{i-1}{2} + 1-2i[/tex]

[tex]= \dfrac{2}{3} i - \dfrac{2}{3} + 1-2i[/tex]

[tex]= \dfrac{1}{3} - \dfrac{4}{3} i[/tex]

Answer: (1/3) - (4/3)i

I might be getting the question wrong. It might be

[tex]\dfrac{\sqrt{-16}}{3 - 3i + (1-2i)}[/tex]

Let's do this one too.

[tex]= \dfrac{4i}{4 - 5i} \cdot \dfrac{4+5i}{4+5i}[/tex]

[tex]= \dfrac{16i - 20}{4^2 + 5^2}[/tex]

[tex]=-\dfrac{20}{41} + \dfrac{16}{41} i[/tex]


The value of the given expression is 7 / 3 - 2i / 3.

What is simplification?

Simplification is to make something easier to do or understand and to make something less complicated.

The expression is given below.

[tex]\rm \Rightarrow \sqrt{\dfrac{-16}{3-3\iota}} + 1 - 2 \iota[/tex]

On simplifying the expression. Then we have

[tex]\rm \Rightarrow \dfrac{\sqrt{-16}}{3-3\iota}+ 1 - 2 \iota\\\\\Rightarrow \dfrac{4 \iota}{3-3\iota}+ 1 - 2 \iota\\\\\Rightarrow \dfrac{4 \iota+ (1 - 2 \iota)(3 - 3 \iota)}{3-3\iota}\\\\\Rightarrow \dfrac{4 \iota+ 3 - 9 \iota -6 \iota ^2 }{3-3\iota}\\\\\Rightarrow \dfrac{4 \iota+ 3 - 9 \iota +6 }{3-3\iota}\\\\\Rightarrow \dfrac{9 - 5 \iota }{3-3\iota}[/tex]

On rationalization, we have

[tex]\Rightarrow \dfrac{9 - 5 \iota }{3-3\iota} \times \dfrac{3+3\iota}{3+3\iota}\\\\\Rightarrow \dfrac{(27 - 15 \iota + 27 \iota - 15 \iota ^2 }{3^2 -3^2\iota ^2} \\\\\Rightarrow \dfrac{(27 - 15 \iota + 27 \iota +15 ) }{9 + 9} \\\\\Rightarrow \dfrac{(42 - 12 \iota ) }{9 + 9} \\\\\Rightarrow \dfrac{(42 - 12 \iota ) }{18} \\\\\Rightarrow \dfrac{7}{3} - \dfrac{2 \iota }{3}[/tex]

Then the value of the given expression is 7 / 3 - 2i / 3.

More about the simplification link is given below.

https://brainly.com/question/12616840

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