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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!
 

 Aug 30, 2019
 #1
avatar+6192 
+3

\(1) ~|zw|^2 = |z|^2 |w|^2 = 16\cdot 4 = 64\\ \left|\dfrac z w \right|^2 = \dfrac{|z|^2}{|w|^2} = \dfrac{16}{4} = 4\\~\\ \text{The remaining two cannot be solved without the angle between $z$ and $w$}\)

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 Aug 31, 2019
 #2
avatar+6192 
+3

\(2)~\text{I assume you mean that $z^*$ is the conjugate of $z$}\\ \text{There's a problem here. If $z^* = 6+8i$ then $|z| = \sqrt{6^2+8^2} = 10$}\\ \text{Yet we are told that $|z|=5$}\\ \text{Is it supposed to be that $z^* w=6+8i$ ?}\)

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 Aug 31, 2019
 #3
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I meant z multiplied by the conjugate of w=6+8i. Sorry for the confusion!!

Guest Sep 4, 2019

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