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Vesnalui [34]
3 years ago
5

What is the solution set for -4x - 10< 2?

Mathematics
1 answer:
Alchen [17]3 years ago
8 0

Answer:

x < -3

Step-by-step explanation:

-4x - 10 < 2

-4x < 12 (+10)

-x < 3 (÷4)

x < 3 (+x, -3)

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Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.
alexandr1967 [171]

For the numbers in a+bi form, convert to polar form:


1+i=\sqrt2\dfrac{1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)

By DeMoivre's theorem,

(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i


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\sqrt3+i=2\dfrac{\sqrt3+i}2=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)

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For the numbers already in polar form, DeMoivre's theorem can be applied directly:


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\left(2(\cos20^\circ+i\sin20^\circ)\right)^3=8\left(\cos60^\circ+i\sin60^\circ\right)=4+4\sqrt3

\left(2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)\right)^4=16(\cos\pi+i\sin\pi)=-16

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