Complex Numbers: Operations

The questions below are due on Wednesday September 18, 2024; 10:00:00 PM.

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Evaluate each of the following expressions. For each, express your answer as a number in the form x+jy. Your answers may make use of pi and sqrt.

(3+5j)\times (-1+3j) = x+jy

x =~

y =~

5e^{j\pi/2}\times (2+2j) = x + jy

x =~

y =~

2e^{j\pi}\times 2e^{j\pi} = x + jy

x =~

y =~

(3+5j) / (-1+3j) = x + jy

x =~

y =~

2e^{j\pi} / 2e^{j\pi\over 2} = x + jy

x =~

y =~

(3+5j)^2 = x + jy

x =~

y =~

(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}j)^j = x + jy

x =~

y =~