Question

I need help with this practice problem solving It is trigonometry The instructions are at the bottom

Answer 1

Being z a complex number:

`z=x+iy`

The modulus of z is:

`\lvert z\rvert=\sqrt[]{x^2+y^2}`

For the given complex number:

`\begin{gathered} z=6-3i \\ \\ \lvert z\rvert=\sqrt[]{6^2+(-3)^2} \\ \lvert z\rvert=\sqrt[]{36+9} \\ \lvert z\rvert=\sqrt[]{45} \\ \\ \text{Simplify:} \\ \lvert z\rvert=\sqrt[]{5\cdot3^2} \\ \lvert z\rvert=3\sqrt[]{5} \end{gathered}`Then, the modulus of the given complex number is 3√5