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the red bubble means I was wrong, but I don't know why

this is the way I did this question

The red bubble means I was wrong, but I don't know why. The second picture is the way I did this question.

Sorry for the inconvenience, I am still learning LaTex.

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    What does $\bar z$ mean? – 2017-02-26
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    It means the conjugate of z – 2017-02-26
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    Note you can upvote any answer that has helped you (using the up-arrow next to the question), and you can accept the most helpful that fully answers your question with the checkmark next to the answer (gives you 2 points also) – 2017-03-02

2 Answers 2

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You are not considered the condition $0\leq\phi<2\pi$. You asked to write the given numbers in the form $r(\cos\phi+i\sin\phi)$ for suitable angle $0\leq\phi<2\pi$.

Though $\bar{z}=7(\cos(-0.5)+i\sin(-0.5) )$ while $-0.5\notin[0,2\pi) $. The correct answer is $\phi=2\pi-0.5 $.

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The angle of the conjugate of $z$ is is always equal to minus the angle of $z$ (because we are reflecting about the $x$ axis). The same happens for the multiplicative inverse (as it is parallel to the conjugate).