SOLUTION: let z be a complex number with arg(z)=theta and |z|=k find the following: i) arg(2z) ii) |z| bar iii) |z^2|/|z| bar iv) arg(z bar * z^2)

Question 1116415: let z be a complex number with arg(z)=theta and |z|=k
find the following:
i) arg(2z)
ii) |z| bar
iii) |z^2|/|z| bar
iv) arg(z bar * z^2)

Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.
let z be a complex number with arg(z)=theta and |z|=k
find the following:

i) arg(2z)              =    (same as  arg(z) );

ii) |z| bar             z bar is the conjugate to z;  therefore, |z| bar = |z|  (same as for z);

iii) |z^2|/|z| bar      = |z|

iv) arg(z bar * z^2)    =    ( same as arg(z) ).

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For introductory lessons on complex numbers, look
    - 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
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.

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