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

User Areim
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2 Answers

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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
√(8), or 2
√(2)

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

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

User Rocco Milluzzo
by
8.3k points
1 vote

Answer:


z=√(8) (cos(45\°) + isin(45\°))

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)((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) }=√(4+4)=√(8)

And the angle is


\theta = tan^(-1)((2)/(2) )\\\theta=tan^(-1)(1)\\\theta = 45\°

Therefore, the polar form of the given complex number is


z=√(8) (cos(45\°) + isin(45\°))

User Subhajit Panja
by
7.5k points

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