91Ó°ÊÓ

Find and plot the complex conjugate of each number. \(-4 i\)

Prove that the conjugate of the quotient of two complex numbers is the quotient of the conjugates. Also prove the corresponding statements for difference and product. Hint: It is casier to prove the statements about product and quotient using the polar coordinate \(r e^{i \theta}\) form ; for the difference, it is easier to use the rectangular form \(x+i y_{\text {. }}\)

Show that the absolute value of a product of two complex numbers is equal to the product of the absolute values. Also show that the absolute value of the quotient of two complex numbers is the quotient of the absolute values. Hint : : Write the numbers in the \(r e^{i \theta}\) form.