De Moivre's Theorem: solve (1 + i)^8 (1 - i*sqrt{3})^(-6)

[Edony]

Hello!

Can anyone help me to slove this:

. . . . .\(\displaystyle (1\, +\, i)^8\, \left(1\, -\, i\, \sqrt{\strut 3\,}\right)^{-6}\)

using De Moivre's Theorem!
Thank you!

 

[Deleted member 4993]

Hello!

Can anyone help me to slove this:

. . . . .\(\displaystyle (1\, +\, i)^8\, \left(1\, -\, i\, \sqrt{\strut 3\,}\right)^{-6}\)

using De Moivre's Theorem!
Thank you!QUOTE]
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[pka]

Can anyone help me to slove this:

. . . . .\(\displaystyle (1\, +\, i)^8\, \left(1\, -\, i\, \sqrt{\strut 3\,}\right)^{-6}\)

using De Moivre's Theorem!

Hints: The polar forms,
\(\displaystyle \Large\sqrt 2 \exp \left( {\frac{{i\pi }}{4}} \right)\;\& \;\frac{1}{2}\exp \left( {\frac{{i\pi }}{3}} \right)\)

 

[Ishuda]

Hello!

Can anyone help me to slove this:

. . . . .\(\displaystyle (1\, +\, i)^8\, \left(1\, -\, i\, \sqrt{\strut 3\,}\right)^{-6}\)

using De Moivre's Theorem!
Thank you!

As a hint,
1 + i = \(\displaystyle \sqrt{2}\, \, [\dfrac{1}{\sqrt{2}}\, +\, \dfrac{1}{\sqrt{2}} i]\)