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(2-2i)^6(sqrt{3}+1)^3/(sqrt{3}+i)^4

 Aug 6, 2015

Best Answer 

 #1
avatar+109765 
+10

$$\\\dfrac{(2-2i)^6(\sqrt{3}+1)^3}{(\sqrt{3}+i)^4}\\\\\\
\dfrac{(2-2i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{(\sqrt{3}+i)^4(\sqrt{3}-i)^4}\\\\\\
\dfrac{2^6(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{\{(\sqrt{3}+i)(\sqrt{3}-i)\}^4}\\\\\\
\dfrac{2^6(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{(3--1)^4}\\\\\\
\dfrac{2^6(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{(4)^4}\\\\\\
\dfrac{2^6(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{(2)^8}\\\\\\$$

 

$$\\\dfrac{(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{4}\\\\\\$$

 

The rest is just painful expansion.  Maybe you do not need to go any further.

(1-i)^6 will work out the easiest.  Use binomial expansions. 

If you need help expanding I suggest you ask for it.   :) 

 Aug 7, 2015
 #1
avatar+109765 
+10
Best Answer

$$\\\dfrac{(2-2i)^6(\sqrt{3}+1)^3}{(\sqrt{3}+i)^4}\\\\\\
\dfrac{(2-2i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{(\sqrt{3}+i)^4(\sqrt{3}-i)^4}\\\\\\
\dfrac{2^6(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{\{(\sqrt{3}+i)(\sqrt{3}-i)\}^4}\\\\\\
\dfrac{2^6(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{(3--1)^4}\\\\\\
\dfrac{2^6(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{(4)^4}\\\\\\
\dfrac{2^6(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{(2)^8}\\\\\\$$

 

$$\\\dfrac{(1-i)^6(\sqrt{3}+1)^3(\sqrt{3}-i)^4}{4}\\\\\\$$

 

The rest is just painful expansion.  Maybe you do not need to go any further.

(1-i)^6 will work out the easiest.  Use binomial expansions. 

If you need help expanding I suggest you ask for it.   :) 

Melody Aug 7, 2015

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