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oksian1 [2.3K]
3 years ago
5

Simplify the given expression below: 4 divided by the quantity of 3 minus 2i

Mathematics
2 answers:
svetoff [14.1K]3 years ago
3 0
This is rationalising the denominator of an imaginary fraction. We want to remove all i's from the denominator.

To do this, we multiply the fraction by 1. However 1 can be expressed in an infinite number of ways. For example, 1 = 2/2 = 3/3 = 4n^2 / 4n^2 (assuming n is not zero!). Let's express 1 as the complex conjugate of the denominator, divided by the complex conjugate of the denominator.

The complex conjugate of (3 - 2i) is (3 + 2i). Then do what I just said:

4/(3-2i) * (3+2i)/(3+2i) = 4(3+2i)/(3-2i)(3+2i) = (12+8i)/(9-4i^2) = (12+8i)/(9+4) = (12+8i)/13

This is the answer you are looking for. I hope this helps :)
vova2212 [387]3 years ago
3 0

Answer:

4/(3-2i) * (3+2i)/(3+2i) = 4(3+2i)/(3-2i)(3+2i) = (12+8i)/(9-4i^2) = (12+8i)/(9+4) = (12+8i)/13

Step-by-step explanation:

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2 years ago
From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th
wel

Answer:

\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}

Step-by-step explanation:

The <u>width</u> of a square is its <u>side length</u>.

The <u>width</u> of a circle is its <u>diameter</u>.

Therefore, the largest possible circle that can be cut out from a square is a circle whose <u>diameter</u> is <u>equal in length</u> to the <u>side length</u> of the square.

<u>Formulas</u>

\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}

\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}

\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}

If the diameter is equal to the side length of the square, then:
\implies \sf r=\dfrac{1}{2}s

Therefore:

\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}

So the ratio of the area of the circle to the original square is:

\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}

Given:

  • side length (s) = 6 in
  • radius (r) = 6 ÷ 2 = 3 in

\implies \sf \textsf{Area of square}=6^2=36\:in^2

\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)

Ratio of circle to square:

\implies \dfrac{28}{36}=\dfrac{7}{9}

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Write the name of the period that has the digits 913.
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The name of period that has the digits 913 is hundreds.<span>
Because Period is considered to a group of places of the digits.</span>

In this case, the given number is 913 and it is the group of hundred because 900 is the highest number it contains.

We can also write 913 as 

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