Rewrite the expression as a complex number in standard form a+bi

Mathematics

1 answer:

emmainna [20.7K]3 years ago

5 0

Answer:

$\textbf{$a + bi = 2 + i$}\\$

Step-by-step explanation:

$\textup{Given:}\\$$\frac{4 + \sqrt{16 - (4)(5)}}{2}$$\\\textup{This can simplified as:}\\\vspace{6mm}\\$

$\frac{4 + \sqrt(-4)}{2}$\vspace{6mm}\\$\implies \frac{4 + 2i}{2}$\vspace{5mm}\\$\implies 2 \left( \frac{2 + i}{2} \right)$\vspace{5mm}\\$$\therefore a + bi = 2 + i$$

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Let C = C1 + C2 where C1 is the quarter circle x^2+y^2=4, z=0,from (0,2,0) to (2,0,0), and where C2 is the line segment from (2,

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Not much can be done without knowing what $\mathbf F(x,y,z)$ is, but at the least we can set up the integral.

First parameterize the pieces of the contour:

$C_1:\mathbf r_1(t_1)=(2\sin t_1,2\cos t_1,0)$
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where $0\le t_1\le\dfrac\pi2$ and $0\le t_2\le1$ . You have

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and so the work is given by the integral

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