Question

z=3 – 43Find the angle 8 (in radians) that makes in the complex plane.Round your answer, if necessary, to the nearest thousandth. Express between - and T.Show Calculator

Answer 1

Given:-

`z=3-4i`

To find:-

The angle.

Complex number will be denoted as,

`z=x+iy`

So the value of x and y are,

`x=3,y=-4`

At first we need to find the value of r.

The formula to calculate r is,

`r=\sqrt[]{x^2+y^2}`

Substituting the values. we get,

`\begin{gathered} r=\sqrt[]{3^2+(-4)^2} \\ r=\sqrt[]{9+16} \\ r=\sqrt[]{25} \\ r=5 \end{gathered}`

Now we use the angle formula,

`\cos \theta=(x)/(r)`

Substituting the value. we get,

`\begin{gathered} \cos \theta=(3)/(5) \\ \end{gathered}`

So the value of theta is,

`\theta=\cos ^(-1)((3)/(5))`