Question

Find the distance between 2+3i and -8+14i

Answer 1

√221

Explanation:

Given the complex numbers z₁ = a₁ + b₁i and z₂ = a₂ + b₂i. The distance between two complex numbers is:

`\displaystyle{d = √(\left(a_2-a_1\right)^2 + \left(b_2-b_1\right)^2)}`

So by applying the formula, we will have:

`\displaystyle{d = √(\left(2+8\right)^2+\left(3-14\right)^2)}\\\\\displaystyle{d=√(10^2+\left(-11\right)^2)}\\\\\displaystyle{d=√(100+121)}\\\\\displaystyle{d=√(221)}`