SOLUTION: Find the modulus and argument of the complex number: (cos2theta + isin2theta)/(2(costheta + isintheta))

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Question 1064976: Find the modulus and argument of the complex number:
(cos2theta + isin2theta)/(2(costheta + isintheta))
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
If you studied complex numbers, you must know that

cos%282theta%29+%2B+i%2Asin%282theta%29 = %28cos%28theta%29+%2B+i%2Asin%28theta%29%29%5E2.


Therefore, the ratio under the question


 = %281%2F2%29%2A%28cos%28theta%29+%2B+i%2Asin%28theta%29%29

The number  %281%2F2%29%2A%28cos%28theta%29+%2B+i%2Asin%28theta%29%29  has the modulus  1%2F2  and the argument  theta.

Solved.


There is a bunch of my lessons on complex numbers
    - 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
    - Raising a complex number to an integer power
    - How to take a root of a complex number
    - Solution of the quadratic equation with real coefficients on complex domain
    - How to take a square root of a complex number
    - Solution of the quadratic equation with complex coefficients on complex domain

    - 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
    - Miscellaneous problems on complex numbers
    - Advanced problem on complex numbers
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".