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which of the following statements are true about the simplified form of the expression (2+2i)÷(1-i)? select all that apply

a) The simplified form is 2i **
b) the simplified form is 4i
c) the simplified form is 2+2i
d) the simplified form is 4+4i
e) the simplified form is a complex number because complex numbers are closed under division
f) the simplified form is not a complex number because complex numbers are not closed under division.

2 answers.

Respuesta :

konrad509

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

So, it's a) for sure. The other one is most likely e), but I'm not sure if it's true in general, that complex numbers are closed under division.

Answer:

Option  and e are correct.

Step-by-step explanation:

Given Expression:

[tex]\frac{2+2i}{1-i}[/tex]

We simplify the given expression to select the correct option.

Consider,

[tex]\frac{2+2i}{1-i}[/tex]

[tex]=\frac{2+2i}{1-i}\times\frac{1+i}{1+i}[/tex]

[tex]=\frac{(2+2i)(1+i)}{(1-i)(1+i)}[/tex]

[tex]=\frac{2-2+i(2+2)}{(1)^2-(i)^2}[/tex]

[tex]=\frac{4i}{1-(-1)}[/tex]

[tex]=\frac{4i}{2}[/tex]

[tex]=2i[/tex]

2i is complex number.

Therefore, Option a and e are correct.

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