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hammer [34]
3 years ago
6

The four vertices of a rectangle drawn on a complex plane are defined by 1 + 4i, -2 + 4i, -2 – 3i, and 1 – 3i. The area of the r

ectangle is square units.
Mathematics
2 answers:
kompoz [17]3 years ago
7 0
The rectangle is 1-(-2) = 3 units in the real direction and 4i-(-3i) = 7 units in the imaginary direction. Its area is 3×7 = 21 square units.
Anna35 [415]3 years ago
5 0

Answer:

The area of rectangle =21 sq units .

Step-by-step explanation:

Given the four vertices of rectangle are 1+4i,-2+4i, -2-3i and 1-3i.

Consider ABCD is  a rectangle and its vertices are 1+4i,-2+4i,-2-3i and 1-3i.

First we find sides of rectangle

AB=vertices of B- vertices of A

AB= -2+4i-(1+4i)=-3

<h3>If complex number=a+bi</h3><h3>Then modulus=\sqrt{a^2+b^2}</h3><h3>Length of AB= \sqrt{(-3)^2}=3 ( Because magnitude = length always positive ) </h3>

BC= Vertices of C - vertices of B

BC=-2-3i-(-2+4i)=-7i

Length of BC=\sqrt{(-7)^2}=7 ( Magnitude always positive)

CD= vertices of D- vertices of C

CD= 1-3i-(-2-3i)=3

Length of CD= \sqrt{3^2}=3 ( Magnitude  always positive)

DA= vertices of A - vertices of D

DA= 1+4i-(1-3i) =7i

Length of DA= \sqrt{7^2}=7 ( Magnitude always positive)

AB=CD and DA= BC

Length BC=7 units

Breadth AB=3 units

Area of the rectangle = length\times breadth

Area of rectangle =AB\times BC

<h3>Area of rectangle= 3\times 7=21 sq units .</h3>
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