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The product of <em>z₁ =</em> 3 · (cos 14π/15 + i · sin 14π/15) and <em>z₂ =</em> 3 √3 · (cos 11π/15 + i · sin 11π/15) in <em>rectangular</em> form with fully simplified expressions is <em>z₁ · z₂ =</em> 7.794 - i · 13.5.
<h3>How to determine the product of two complex numbers</h3>
Let be two numbers of the form <em>z = a + i · b</em>, where <em>i =</em> √-1, the product of two of these numbers in <em>rectangular</em> form is described by the following formula:
<em>z₁ · z₂ = (a + i · b) · (c + i · d) = (a · c - b · d) + i · (a · d + b · c)</em> (1)
If we know that a = 3 · cos 14π/15, b = 3 · sin 14π/15, c = 3√3 · cos 11π/15, d = 3√3 · sin 11π/15, then the result in rectangular form is:
<em>z₁ · z₂ =</em> 7.794 - i · 13.5
The product of <em>z₁ =</em> 3 · (cos 14π/15 + i · sin 14π/15) and <em>z₂ =</em> 3 √3 · (cos 11π/15 + i · sin 11π/15) in <em>rectangular</em> form with fully simplified expressions is <em>z₁ · z₂ =</em> 7.794 - i · 13.5.
<h3>Remark</h3>
The statement presents typing mistakes and is poorly formatted, the correct form is introduced below:
<em>Given the complex number z₁ = 3 · (cos 14π/15 + i · sin 14π/15) and z₂ = 3 √3 · (cos 11π/15 + i · sin 11π/15), express the result of z₁ · z₂ in rectangular form with fully simplified fractions and radicals.</em>
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To learn more on complex numbers, we kindly invite to check this verified question: brainly.com/question/10251853
Step-by-step explanation:
ED is greater than BC
the line from B to ED ^ (which i drew ) the point it touches ED name it X. so EX will be 2 ( ED-BC)(6-4).
then u have a triangle. EX, XB and EB.
you have length of EX(2) and u have hypotenuse. so u can calculate XB using Pythagoras theorem.
15.1²=2²+XB²
15.1²-2²=XB²
224.01=XB²
XB=14.97
since XB and DC are parallel ( a rectangle is forming XBCD) so DC is also 14.97
