Given:
There are given that complex numbers:
[tex]\begin{gathered} G=3i \\ O=2+5i \\ B=5-i \\ U=-1-4i \\ C=-6 \\ S=-4+2i \end{gathered}[/tex]
Explanation:
According to the question:
We need to find the absolute value of the all above given complex numbers:
So,
To find the absolute value of the complex number, we need to use the properties of the complex number:
So,
From the properties of the complex numbers:
[tex]|a+ib|=\sqrt{a^2+b^2}[/tex]
So,
From the first complex number:
[tex]\begin{gathered} G=3\imaginaryI \\ |G|=\sqrt{0^2+3^2} \\ |G|=\sqrt{9} \\ |G|=3 \end{gathered}[/tex]
From the second complex number:
[tex]\begin{gathered} O=2+5\imaginaryI \\ |O|=\sqrt{2^2+5^2} \\ |O|=\sqrt{4+25} \\ |O|=\sqrt{29} \end{gathered}[/tex]
From the third complex number:
[tex]\begin{gathered} B=5-\imaginaryI \\ |B|=\sqrt{5^2+(-1)^2} \\ |B|=\sqrt{25+1} \\ |B|=\sqrt{26} \end{gathered}[/tex]
From the fourth complex number:
[tex]\begin{gathered} U=-1-4\imaginaryI \\ |U|=\sqrt{(-1)^2+(-4)^2} \\ |U|=\sqrt{1+16} \\ |U|=\sqrt{17} \end{gathered}[/tex]
From the fifth complex number:
[tex]\begin{gathered} C=-6 \\ |C|=\sqrt{(-6)^2+0^2} \\ |C|=\sqrt{36} \\ |C|=6 \end{gathered}[/tex]
Then,
From the sixth complex number:
[tex]\begin{gathered} S=-4+2\imaginaryI \\ |S|=\sqrt{(-4)^2+(2)^2} \\ |S|=\sqrt{16+4} \\ |S|=\sqrt{20} \end{gathered}[/tex]
Final answer:
Hence, the absolute of the given complex number is shown below:
[tex]\begin{gathered} \lvert G\rvert=3 \\ \lvert O\rvert=\sqrt{29} \\ \lvert B\rvert=\sqrt{26} \\ \lvert U\rvert=\sqrt{17} \\ \lvert C\rvert=6 \\ \lvert S\rvert=\sqrt{20} \end{gathered}[/tex]
