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find the argument of z=443iz=-4-4^3i

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Q. find the argument of z=443iz=-4-4^3i
  1. Identify parts of zz: Identify the real and imaginary parts of z=443iz=-4-4^3i.\newlineReal part: 4-4\newlineImaginary part: 43=64-4^3 = -64
  2. Calculate argument of z: Calculate the argument of zz, which is the angle θ\theta in the polar form of the complex number.\theta = \arctan\left(\frac{\text{Imaginary part}}{\text{Real part}}\right) = \arctan\left(\frac{\(-64\)}{\(-4\)}\right)
  3. Simplify fraction for arctan: Simplify the fraction inside the arctan function. \(\arctan\left(\frac{-64}{-4}\right) = \arctan(16)
  4. Use calculator to find value: Use a calculator to find the value of arctan(16)\arctan(16).θarctan(16)1.51\theta \approx \arctan(16) \approx 1.51 radians

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