SOLUTION: If z1 = 4cis300° and z2 = 2cis30° , find z1z2 in its POLAR FORM: rcis(theta).

Question 1180641: If z1 = 4cis300° and z2 = 2cis30° , find z1z2 in its POLAR FORM: rcis(theta).
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
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If z1 = 4cis300° and z2 = 2cis30° , find z1z2 in its POLAR FORM: rcis(theta).
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The rule of multiplication of complex numbers, written in polar form, is THIS:


    +------------------------------------------------------+
    |    The product of complex numbers is the product     | 
    |    of their modules and the sum of their arguments.  |
    +------------------------------------------------------+


or, in mathematical form

    r*cis(a) * R*cis(b) = rR*cis(a+b)



In your problem

    z1 * z2 = 4cis(300°)*2cis(30°) = 8cis(330°).

Solved.

-----------------

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.

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