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The "solution" by @MathLover1 is A B S O L U T E L Y W R O N G.
So I came to bring a correct solution.
We are given a complex number z; Let be the complex conjugate to z complex number.
Then |z-1|^2 = = - + 1 = |z|^2 - 2*Re(z) + 1. ANSWER
Here Re(z) is the real part of the complex number z.
Solved.
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On complex numbers, see introductory lessons
- Complex numbers and arithmetical operations on them
- Complex plane
- Addition and subtraction of complex numbers in complex plane
- Multiplication and division of complex numbers in complex plane
- Solved problems on taking roots of complex numbers
- Solved problems on arithmetic operations on complex numbers
- Solved problem on taking square root of complex number
in this site.
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Complex numbers".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.