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Vsevolod [243]
2 years ago
6

What is the imaginary part of z?

Mathematics
1 answer:
Shkiper50 [21]2 years ago
8 0

Answer:

The imaginary part is the multiple of i. It is common practice to use the letter z to stand for a complex number and write z = a + bi where a is the real part and b is the imaginary part. where a is the real part and b is the imaginary part.

Step-by-step explanation:

You can easily check that a complex number z = x + yi times its conjugate x – yi is the square of its absolute value |z|2. Therefore, 1/z is the conjugate of z divided by the square of its absolute value |z|2.

Complex numbers A complex number z is defined as an ordered pair z = (x, y), where x and y are a pair of real numbers.

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The quadrilateral is a trapezoid and the area of the quadrilateral is 85.04 square units

<h3>How to determine the quadrilateral?</h3>

The vertices are given as:

A:(-2, 3) B:(4, -6) C:(10, 2) D:(6, 8)

Next, we plot the vertices (see attachment)

From the attached graph, we can see that the quadrilateral is a trapezoid

<h3>How to determine the area?</h3>

From the plot, we have the following features:

Height: AD

Parallel sides: CD and AB

Calculate the lengths using:

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

So, we have:

AD = \sqrt{(-2 -6)^2 + (3 -8)^2}

AD = \sqrt{89}

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CD = \sqrt{52}

AB = \sqrt{(-2 -4)^2 + (3 +6)^2}

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The area is then calculated as:

Area = 0.5 * (CD + AB) * AD

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Area = 0.5 * (√52 + √117) * √89

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Area = 85.04

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Read more about areas at:

brainly.com/question/24487155

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