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2 years ago

Find the product Please help me

Mathematics

2 answers:

Evgen [1.6K]2 years ago

7 0

Answer 4a+6b=ab

Step-by-step explanation:

ExtremeBDS [4]2 years ago

6 0

Answer:

4a^2-4ab+6ab-6b^2

4a^2+2ab-6b^2

hope this helps :)

Step-by-step explanation:

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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,

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

$-1+i=\sqrt2\dfrac{-1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4}\right)$

$\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i$

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

$\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)$

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

$2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3$

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

At second glance, I think the 2s in the last two numbers should also be getting raised to the 3rd and 4th powers:

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

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

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2 years ago

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none of the above

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2 years ago

If you invested $250 at 16% interest, how much will you have after 18 years?

Whitepunk [10]

After 1st year: 250$:100%=x$:116%, 250$*116%=x$*100%, x=(250*116)/100=290$. After 1st year I will have 290$
After 2nd year: 290$:100%=x$:116%, x=(290*116)/100=336.4$. After 2nd year I will have 336.4$
After 3rd year I will have (336.4*116)/100=390.224$
After 4th yr: (390.224*116)/100=452.65984$
After 5th yr: (452.65984*116)/100=525.085$
After- 6th yr: 609.1$, 7th yr: 706.556$, 8th yr: 819.605$, 9th yr: 950.742$
10th yr: 1102.86$, 11th yr: 1279.32$, 12th yr: 1484.01$, 13th yr: 1721.45$,
14th yr: 1996.88$, 15th: 2316.38$, 16th yr: 2687$, 17th yr: 3116.92$
After 18 years I will have 3615.63$.

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3 years ago

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