hmmm first off let's convert the √3 +i to trigonometric form, and then use De Moivre's root theorem, bearing in mind that √3 and i or 1i are both positive, meaning we're on the I Quadrant.

$\bf (\stackrel{a}{\sqrt{3}}~,~\stackrel{b}{1i})\qquad \begin{cases} r=&\sqrt{(\sqrt{3})^2+1^2}\\ &\sqrt{3+1}\\ &2\\ \theta =&tan^{-1}\left( \frac{1}{\sqrt{3}}\right)\\\\ &tan^{-1}\left( \frac{\sqrt{3}}{3} \right)\\ &\frac{\pi }{6} \end{cases}~\hfill \implies ~\hfill 2\left[ cos\left( \frac{\pi }{6}\right) +i~sin\left( \frac{\pi }{6}\right) \right]$

$\bf ~\dotfill\\\\ \qquad \textit{power of two complex numbers} \\\\\ [\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)] \\\\[-0.35em] ~\dotfill$

$\bf \left[ 2\left[ cos\left( \frac{\pi }{6}\right) +i~sin\left( \frac{\pi }{6}\right) \right] \right]^3\implies 2^3\left[ cos\left( 3\cdot \frac{\pi }{6}\right) +i~sin\left( 3\cdot \frac{\pi }{6}\right) \right] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 8\left[cos\left( \frac{\pi }{2} \right) +i~sin\left( \frac{\pi }{2} \right) \right]~\hfill$

3 0

4 years ago

Gayle is making gift bags and must tie 250 ribbons to them. If Gayle can tie 4 ribbons every 10 minutes, how long will it take G

mart [117]

Answer:

625 minutes

Step-by-step explanation:

Given that:

Time taken to tie 4 ribbons = 10 minutes

Number of ribbons to be tied = 250

To find:

Time taken to tie 250 ribbons.

Solution:

First of all, we need to find the time taken to tie one ribbon.

And then we can multiply it with 250 to find the time taken to tie all the 250 ribbons.

For finding the time to tie one ribbon, we need to divide the time taken to tie 4 ribbons with 4.

Time taken to tie 1 ribbon = $\frac{10}{4} = 2.5$ minutes

Time taken to tie 250 ribbons = 2.5 $\times$ 250 = <em>625 minutes</em>

4 0

3 years ago

If f (1)= -2, then the point is on the graph of f

Komok [63]

<h3>Answer: (1, -2)</h3>

Explanation:

Writing f(1) = -2 means x = 1 and y = f(x) = -2 pair up together

So we have (x,y) = (1, -2) as the point on the f(x) curve.

6 0

3 years ago

Subject - Maths<br><br>Need help!

xeze [42]

1) 25%

2) 60

3) 1750

5) 20%

6) 2400

7) 10

8)24

9) 1/25

10) X/y = constant.

sorry 4 no. is not taught in Nepal

5 0

3 years ago

Read 2 more answers