Which expression is equivalent to (3x - 4)(4x - 3)?

Mathematics

1 answer:

Ulleksa [173]3 years ago

7 0

Answer:

1\/48 (24 x - 25)^2 - 49\/48

x (12 x - 25) + 12

Step-by-step explanation:

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Solve using demoivres theorem

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It's difficult to make out, but I think the task is to expand

$(\sqrt3-i)^4$

Write the number in polar form first:

$\sqrt3-i=2e^{-i\pi/6}$

By DeMoivre's theorem, you have

$(\sqrt3-i)^4=\left(2e^{-i\pi/6}\right)^4=2^4e^{-i4\pi/6}=16e^{-i2\pi/3}$

and converting back to Cartesian form, this number is equivalent to

$16\left(\cos\dfrac{2\pi}3-i\sin\dfrac{2\pi}3\right)=16\left(-\dfrac12+-\dfrac{\sqrt3}2\right)=-8(1+i\sqrt3)$