Express z_(1)=-8sqrt3+8i in polar form. Express your answer in exact terms, using degrees, where your angle is between 0^(@) and 360^(@), inclusive. z_(1)=

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Express  z_(1)=-8sqrt3+8i in polar form. Express your answer in exact terms, using degrees, where your angle is between  0^(@) and  360^(@), inclusive.  z_(1)=

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Identify Coordinates: Identify the rectangular coordinates of the complex number. The complex number z_(1) = -8√3 + 8i has rectangular coordinates (-8√3, 8).Calculate Magnitude: Calculate the magnitude (r) of the complex number. The magnitude is found using the formula r = √(x^2 + y^2), where x and y are the real and imaginary parts, respectively. r = √((-8√3)^2 + 8^2) r = √(64*3 + 64) r = √(192 + 64) r = √256 r = 16Find Argument in Radians: Calculate the argument (θ) of the complex number in radians. The argument is found using the formula θ = atan2(y, x). θ = atan2(8, -8√3) Since the complex number is in the second quadrant (negative real part, positive imaginary part), the angle θ will be between 90° and 180°.Convert to Degrees: Convert the argument to degrees. To convert radians to degrees, we use the formula degrees = radians * (180/π). However, we can directly calculate the angle in degrees using the atan2 function and considering the quadrant. θ = atan2(8, -8√3) = 135° (since it is in the second quadrant)Express in Polar Form: Express the complex number in polar form. The polar form of a complex number is z = r(cos(θ) + i*sin(θ)), where r is the magnitude and θ is the argument. Using the magnitude and argument calculated, the polar form is: z_(1) = 16(cos(135°) + i*sin(135°))

Express $z_{1}=-8 \sqrt{3}+8 i$ in polar form. $\newline$ Express your answer in exact terms, using degrees, where your angle is between $0^{\circ}$ and $360^{\circ}$ , inclusive. $\newline$ $z_{1}=$

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Express $z_{1}=-8 \sqrt{3}+8 i$ in polar form. $\newline$ Express your answer in exact terms, using degrees, where your angle is between $0^{\circ}$ and $360^{\circ}$ , inclusive. $\newline$ $z_{1}=$