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Part a) Let z and w be complex numbers satisfying |z| = 4 and |w| = 2. What is $$|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2$$?

Part b) Let z and w be complex numbers satisfying |z| = 5, |w| = 2, and $$z\overline{w} = 6+8i.$$ What is $$|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2$$?

Dec 22, 2019