SOLUTION: Compute |3+4i|+|3-4i|+|-3+4i|+|-3-4i|. I'm confused on the absolute value and how it ties in, can you please help me? Thanks.

Question 1171210: Compute
|3+4i|+|3-4i|+|-3+4i|+|-3-4i|.
I'm confused on the absolute value and how it ties in, can you please help me? Thanks.
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

Each of the four given complex numbers (points) on the complex plane
represents a right angled triangle, namely, (3,4,5)-triangle
with the legs of 3 and 4 units long and the hypotenuse of 5 units long.

Everybody who works with complex numbers MUST know it.

So the 4 addends represent 5 unit long segment, each.

Therefore, the entire sum is 5 + 5 + 5 + 5 = 4*5 = 20 units.

.............

Solved, explained and completed.

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

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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