Question

Am I correct? I need some clarification on this practice problem solving I have attempted this problem but for some reason I feel like I may be wrong

Answer 1

The modulus of a complex number;

`z=a+bi`

is denoted by;

`|z|=|a+bi|=\sqrt[]{a^2+b^2}`

Thus, given the complex number;

`2-6i`

The modulus is;

`\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*10} \\ |2-6i|=\sqrt[]{4}*\sqrt[]{10} \\ |2-6i|=2*\sqrt[]{10} \\ |2-6i|=2\sqrt[]{10} \end{gathered}`

ANSWER:

`2\sqrt[]{10}`