Express z_(1)=-14+14 i 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)=-14+14 i 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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Calculate Magnitude: To express a complex number in polar form, we need to find its magnitude (r) and angle (θ). The magnitude is found using the formula r = √(a^2 + b^2), where a is the real part and b is the imaginary part of the complex number. For z_(1) = -14 + 14i, we have a = -14 and b = 14. Now we calculate the magnitude: r = √((-14)^2 + (14)^2) = √(196 + 196) = √(392) = 14√2.Find Angle: Next, we need to find the angle θ. The angle is determined by the arctan function, θ = arctan(b/a). However, since the complex number is in the second quadrant (a is negative and b is positive), we need to add 180 degrees to the angle found by arctan(b/a) to get the correct angle in the range of 0 to 360 degrees. θ = arctan(14 / -14) + 180° = arctan(-1) + 180°. We know that arctan(-1) corresponds to -45 degrees (or 315 degrees if we want a positive angle), so θ = -45° + 180° = 135°.Write in Polar Form: Now we can write the complex number in polar form. The polar form is given by z = r(cos(θ) + i*sin(θ)), where r is the magnitude and θ is the angle. For z_(1), the polar form is z_(1) = 14√2(cos(135°) + i*sin(135°)).

Express $z_{1}=-14+14 i$ 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 z1=−14+14i z_{1}=-14+14 i z1​=−14+14i in polar form.\newlineExpress your answer in exact terms, using degrees, where your angle is between 0∘ 0^{\circ} 0∘ and 360∘ 360^{\circ} 360∘, inclusive.\newlinez1= z_{1}= z1​=

Express $z_{1}=-14+14 i$ in polar form. $\newline$ Express your answer in exact terms, using degrees, where your angle is between $0^{\circ}$ and $360^{\circ}$ , inclusive. $\newline$ $z_{1}=$