Given:
[tex]|3+4 i|+|3-4 i|+|-3+4 i|+|-3-4 i|[/tex]
Solution:
Complex formula:
[tex]|a+b i|=\sqrt{(a+b i)(a-b i)}=\sqrt{a^{2}+b^{2}}[/tex]
Let us simplify one by one.
[tex]|3+4 i|=\sqrt{3^{2}+4^{2}}[/tex]
[tex]=\sqrt{25}[/tex]
|3 + 4i| = 5
[tex]|3-4 i|=\sqrt{3^{2}+(-4)^{2}}[/tex]
[tex]=\sqrt{25}[/tex]
|3 - 4i| = 5
[tex]|-3+4 i|=\sqrt{(-3)^{2}+4^{2}}[/tex]
[tex]=\sqrt{25}[/tex]
|-3 + 4i| = 5
[tex]|-3-4 i|=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]
[tex]=\sqrt{25}[/tex]
|-3 - 4i| = 5
Substitute these in the given expression:
[tex]|3+4 i|+|3-4 i|+|-3+4 i|+|-3-4 i|=5+5+5+5[/tex]
[tex]=20[/tex]
The solution of the expression is 20.
