Question

what is the distance from the origin to point p graphed on the complex plane?
options:
\\(\sqrt{29}\\)
7
\\(\sqrt{7}\\)
29

Explanation:

Step1: Identify coordinates of P

From the complex plane, point P has coordinates \((-5, -2)\) (x = -5, y = -2, where x is real part, y is imaginary part).

Step2: Apply distance formula

Distance from origin \((0,0)\) to \((x,y)\) is \(d = \sqrt{(x - 0)^2 + (y - 0)^2}\). Substitute \(x = -5\), \(y = -2\):
\(d = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29}\).

Answer:

\(\sqrt{29}\) (corresponding to the option with \(\sqrt{29}\))