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Andrew [12]
3 years ago
13

Write the complex number in polar form. express the argument in degrees, rounded to the nearest tenth, if necessary. 5) 2 +2i

Mathematics
2 answers:
horrorfan [7]3 years ago
7 0

Answer:

z=\sqrt{8} (cos(45\°) + isin(45\°))

Step-by-step explanation:

The polar form of a complex number is

z=r(cos\theta + isin\theta)

Where r=\sqrt{a^{2} +b^{2} }, a=rcos\theta, b=rsin\theta and \theta = tan^{-1}(\frac{b}{a} )

In this case, we have the number 2+2i, where a=2 and b=2, so the module r is

r=\sqrt{a^{2} +b^{2} }=\sqrt{2^{2} +2^{2} }=\sqrt{4+4}=\sqrt{8}

And the angle is

\theta = tan^{-1}(\frac{2}{2} )\\\theta=tan^{-1}(1)\\\theta = 45\°

Therefore, the polar form of the given complex number is

z=\sqrt{8} (cos(45\°) + isin(45\°))

Goryan [66]3 years ago
4 0
Here you need to calculate the magnitude and phase angle of the quantity 2 + 2i.

The magnitude is found using the Pyth. Thm. and is sqrt(2^2 + 2^2), or \sqrt{8}, or 2\sqrt{2}

Recognize that the phase angle is 45 deg, or \pi/4 rad.

Thus, the complex form is (2sqrt(2) angle \pi/4   rad ).

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