Hi, I am very stuck on the following 2 problems. Help would be appreciated!
1) Let z and w be complex numbers satisfying |z| = 4 and |w| = 2. Then enter in the numbers |z+w|^2, |zw|^2, |z-w|^2, |z/w|^2 below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark.
2) Let z and w be complex numbers satisfying |z| = 5, |w| = 2, and z*(conjugate of w) = 6+8i. Then enter in the numbers |z+w|^2, |zw|^2, |z-w|^2, |z/w|^2 below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark.
Thanks in advance for the help!
+6251 \(1) ~|zw|^2 = |z|^2 |w|^2 = 16\cdot 4 = 64\\ \left|\dfrac z w \right|^2 = \dfrac{|z|^2}{|w|^2} = \dfrac{16}{4} = 4\\~\\ \text{The remaining two cannot be solved without the angle between $z$ and $w$}\)
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