5. Simplify to give the answer in polar form and in rectangular form:
\[
\frac{(2-j)^{4}(-\sqrt{3}+j)^{3}}{(-1-j)^{5}}
\]

Answer

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Answer

Convert the result back to rectangular form: \(\boxed{17.00 - 31.00j}\).

Steps

Step 1 ：Convert each complex number to its polar form: \(z_1 = 2 - j\), \(z_2 = -\sqrt{3} + j\), and \(z_3 = -1 - j\).

Step 2 ：Find the polar forms: \(z_1 = \left(2.24, -0.46\right)\), \(z_2 = \left(2, 2.62\right)\), and \(z_3 = \left(1.41, -2.36\right)\).

Step 3 ：Use the properties of exponents to simplify the expression: \(\frac{z_1^4 z_2^3}{z_3^5}\).

Step 4 ：Calculate the result in polar form: \(\left(35.36, 17.78\right)\).

Step 5 ：Convert the result back to rectangular form: \(\boxed{17.00 - 31.00j}\).