What is the distance between 1 + 3i and 2 - 4i in the complex plane?
O V10
© 21/10
41n13
sara

5√(2)

Step-by-step explanation:

The distance between the two complex number is just the magnitude of the difference between the two complex number.

Basically subtract them with each other and find the magnitude of their difference.

You treat the real value like a x-component, and the imaginary value like a y-component.

Z₁ = 1 + 3i

Z₂ = 2 - 4i

Z₂ - Z₁ = (2 - 4i) - (1 + 3i) = -1 - 7i

This is just the distance formula. Remember that the real value can be treated like an x-value and imaginary component can be treated like a y-value.

|Z₂ - Z₁| = √((Real)² + (Imaginary)²)

|Z₂ - Z₁| = √((-1)² + (-7)²)

= √(50)

= √(25·2)

= 5√(2)

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: