Question

what is the length of the radius of a circle with a center at the origin and a point on the circle at 8 + 15i?

1. $sqrt{7}$
2. $sqrt{15}$
3. 15
4. 17

Explanation:

Step1: Recall distance formula for complex numbers

The distance $d$ from the origin $(0 + 0i)$ to a complex number $a+bi$ is given by $d=\sqrt{a^{2}+b^{2}}$. Here $a = 8$ and $b = 15$.

Step2: Calculate the radius

Substitute $a = 8$ and $b = 15$ into the formula: $r=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17$.

Answer:

D. 17