Question

Find the distance between the complex numbers. z1 = 9 - 9i z2 = 10 - 9i

Answer 1

Answer:

The distance between the two given complex numbers = 9

Step-by-step explanation:

Explanation:-

Step(i):-

Given  Z₁ = 9 - 9 i    and Z₂ = 10 -9 i

Let A and B represent complex numbers Z₁ and Z₂ respectively on the argand plane

⇒ A =  Z₁ = x₁ +i y₁ = 9 - 9 i and

    B = Z₂ = x₂+ i y₂ = 10 -9 i

Let (x₁ , y₁) = ( 9, -9)

     (x₂, y₂) = (10, -9)

Step(ii):-

The distance between the two points are

    A B   =   $\sqrt{(x_{2} - x_{1})^{2}+(y_{2} - y_{1})^{2} }$

    A B =   $\sqrt{(10 - 1)^{2}+(-9 - (-9))^{2} }$

   AB   = $\sqrt{(9)^{2} +(-9+9)^{2} }$

  AB    =  √81 = 9

Conclusion:-

The distance between the two given complex numbers = 9