Given:-
[tex]z=3-4i[/tex]
To find:-
The angle.
Complex number will be denoted as,
[tex]z=x+iy[/tex]
So the value of x and y are,
[tex]x=3,y=-4[/tex]
At first we need to find the value of r.
The formula to calculate r is,
[tex]r=\sqrt[]{x^2+y^2}[/tex]
Substituting the values. we get,
[tex]\begin{gathered} r=\sqrt[]{3^2+(-4)^2} \\ r=\sqrt[]{9+16} \\ r=\sqrt[]{25} \\ r=5 \end{gathered}[/tex]
Now we use the angle formula,
[tex]\cos \theta=\frac{x}{r}[/tex]
Substituting the value. we get,
[tex]\begin{gathered} \cos \theta=\frac{3}{5} \\ \end{gathered}[/tex]
So the value of theta is,
[tex]\theta=\cos ^{-1}(\frac{3}{5})[/tex]
