Question: Write the following complex number in the form a + bi and also in polar form. Write exact answers (no decimals), including all arguments.

Write the following complex number in the form a + bi and also in polar form. Write exact answers (no decimals), including all arguments. a. b. (1+i)(1-3i)(3+i) C. 3 i + i d. 1 + 2i 3-4i A complex number with argument 12 and real part 1 a. Prove that (z) = (zk), z 0 for all k Z and all z E C. (Hint: z = re.) b. Use the previous part to show that if zo is a root of the equation anz+an-12-1+...+az+ao a solution. = 0, where all the coefficients are real numbers, then zo is also

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