Express the complex number in trigonometric form. square root of 3+2i

1 answer:

8 0

$\bf \begin{array}{llll}
\sqrt{3}&,&2i\\
\uparrow &&\uparrow \\
a&&b
\end{array}\implies r[cos(\theta )+i\ sin(\theta )]\qquad 
\begin{cases}
r=\sqrt{a^2+b^2}\\
\theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}
\\\\\\
r=\sqrt{(\sqrt{3})^2+(2)^2}\implies r=\sqrt{3+4}\implies r=\sqrt{7}
\\\\\\
\theta =tan^{-1}\left( \frac{2}{\sqrt{3}} \right)\implies \theta \approx 49.10660535^o\textit{ or just 49 rounded up}\\\\
-------------------------------\\\\
\sqrt{3},2i\implies \sqrt{7}[cos(49^o)+i\ sin(49^o)]$

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Enter the values for m, n, and p that complete the difference:

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Answer:

p = 2

n = 14

m = 3

Step-by-step explanation:

In order to be able combine (either add or subtract) rational expressions we need to write them with a common (similar) denominator. For that reason we first find the Least Common Denominator of both fractions, that way understanding how to express the two fractions using equivalent fractions with like denominator that can be combined.

We see that the denominator of the first fraction contains the factor "x", therefore "x" has to be a factor of that least common denominator.

We also see that the second fraction contains "2" as a factor, therefore 2 has to be a factor as well for our Least Common Denominator (LCD)

So the LCD we need is the product: 2*x which we write as 2x.

Now we write the first fraction as an equivalent one but with denominator "2x" by multiplying top and bottom by 2 (and thus not changing the actual value of the fraction): $\frac{7}{x} =\frac{7*2}{x*2} =\frac{14}{2x}$