Solution:
The modulus of a complex number;
[tex]z=a+bi[/tex]
is denoted by;
[tex]|z|=|a+bi|=\sqrt[]{a^2+b^2}[/tex]
Thus, given the complex number;
[tex]2-6i[/tex]
The modulus is;
[tex]\begin{gathered} a=2,b=-6 \\ |2-6i|=\sqrt[]{2^2+(-6)^2} \\ |2-6i|=\sqrt[]{4+36} \\ |2-6i|=\sqrt[]{40} \\ |2-6i|=\sqrt[]{4\times10} \\ |2-6i|=\sqrt[]{4}\times\sqrt[]{10} \\ |2-6i|=2\times\sqrt[]{10} \\ |2-6i|=2\sqrt[]{10} \end{gathered}[/tex]
ANSWER:
[tex]2\sqrt[]{10}[/tex]
