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3 years ago

Solve the equation -(-2-n)

Mathematics

1 answer:

Harrizon [31]3 years ago

8 0

Answer:

<h2><u><em>I think 2 + n</em></u></h2>

Step-by-step explanation:

<h2><u><em> Step1: Distribute parentheses -(-2)-(-n)</em></u></h2><h2><u><em>Step 2: Then Apply minus - plus rules and u will get -(-a)=a</em></u></h2><h2><u><em>step 3: = 2+n</em></u></h2>

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Step-by-step explanation:

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3 years ago

Find all the complex roots. Write the answer in exponential form.

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$\begin{gathered} r=\sqrt[]{9^2+(9\sqrt[]{3})^2} \\ r=\sqrt[]{81+81\cdot3} \\ r=\sqrt[]{81+243} \\ r=\sqrt[]{324} \\ r=18 \end{gathered}$ $\theta=\arctan (\frac{9\sqrt[]{3}}{9})=\arctan (\sqrt[]{3})=\frac{\pi}{3}$

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$z^{\frac{1}{n}}=r^{\frac{1}{n}}\cdot\lbrack\cos (\frac{\theta+2\pi k}{n})+i\cdot\sin (\frac{\theta+2\pi k}{n})\rbrack\text{ for }k=0,1,\ldots,n-1$

Then, for a fourth root, we will have n = 4 and k = 0, 1, 2 and 3.

To simplify the calculations, we start by calculating the fourth root of r:

$r^{\frac{1}{4}}=18^{\frac{1}{4}}=\sqrt[4]{18}$

<em>NOTE: It can not be simplified anymore, so we will leave it like this.</em>

Then, we calculate the arguments of the trigonometric functions:

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We can now calculate for each value of k:

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Answer:

The four roots in exponential form are

z0 = 18^(1/4)*e^(i*π/8)

z1 = 18^(1/4)*e^(i*5π/8)

z2 = 18^(1/4)*e^(i*9π/8)

z3 = 18^(1/4)*e^(i*13π/8)

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3 years ago