All categories

3 years ago

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

2 answers:

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:

You might be interested in

What is 75percent of 200

Setler79 [48]

Answer:

150

Step-by-step explanation:

4 0

2 years ago

Solve for x: X= 76⁰ 9x+1 40°

luda_lava [24]

7 is the value of x, and 64° is the measure of the unknown angle.

Triangle angles of 76°, (9x+1)°, and 40° are provided.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.

Now, the total of a triangle's three angles equals

76°+(9x+1)°+40°= 180°

⇒ 116+9x+1 = 180

⇒ 9x + 117 = 180

⇒ 9x = 63

⇒ x = 7

So, 9x+1=64°

As a result, x is equal to 7 and the unmeasured angle is 64°.

To learn more about the angle sum property of a triangle, refer to this link:

brainly.com/question/8492819

#SPJ1

4 0

1 year ago

What is the amplitude, period, and phase shift of f(x) = -4 sin(2x + π) - 5?

son4ous [18]

F(x) = -4sin(2x + π) - 5

Amplitude
A = -π

Period
2π = 2π = π
B 2

Phase Shift
-C = -π = ≈ 1.57
 B 2

3 0

3 years ago

Read 2 more answers

A student organization wondered how many hours per week college students study during a term. Each of the 10 students in the org

Inga [223]

Answer:

No, a convenience sample was taken.Therefore, the sample may not be representative of all college students in terms of number of hours studied per week.

Step-by-step explanation:

One of the important conditions required in other to estimate the mean of the population from the confidence interval. Requires that the data must be a random Sample. This is to ensure that sample values are not biased and as such are representative of the larger group of data.

However, in the scenario described above, the sample chose. Are friend's of the student, this makes the data lack randomness as those who aren't friends to the student do not stand a chance of being selected. The sampling procedure employed is called convenience sampling.

4 0

3 years ago

???????anyone know...

RUDIKE [14]

The answer is: " 60° " .
__________________________________________________________
" m∠A = 60° " .
__________________________________________________________
Explanation:
__________________________________________________________

Note: All triangles, by definition, have 3 (three) sides and 3 (three angles).

The triangle shown (in the "image attached") has three EQUAL side lengths. Therefore, the triangle shown is an "equilateral triangle" and has 3 (three) equal angles, as well.

All triangles by, definition, have 3 (three) angles that add up to "180° " .

Since each of the 3 (three) angles is equal; and the three angles are:

"∠A" , "∠B" , and "∠C" ;

We can find the measure of "∠A" ; denoted as: "m∠A" ; as follows:
______________________________________________________
m∠A = 180° ÷ 3 = 60° .
______________________________________________________
The answer is: " 60° " .
______________________________________________________
m∠A = " 60° " .
______________________________________________________

7 0

3 years ago