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Novay_Z [31]
3 years ago
13

Simplify (10 + 3i)(5 − 2i).

Mathematics
2 answers:
Romashka [77]3 years ago
6 0
The answer I think is D but use the app photo math very useful:)
kirza4 [7]3 years ago
6 0

Answer:  The correct option is

(C) 56-5i.

Step-by-step explanation:  We are given to simplify the following product of complex numbers :

P=(10+3i)(5-2i)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

To simplify the given product, we must multiply each term of the first factor each term of the second factor and will be using the following vale of i :

i=\sqrt{-1}~~~~\Rightarrow i^2=-1.

From (i), we get

P\\\\=(10+3i)(5-2i)\\\\=10(5-2i)+3i(5-2i)\\\\=50-20i+15i-6i^2\\\\=50-5i-6(-1)\\\\=50-5i+6\\\\=56-5i.

Thus, the required simplified form is 56-5i.

Option (C) is CORRECT.

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The complete proof for the given parallelogram is given in the image attached below.

<h3>What is a Parallelogram?</h3>

A parallelogram is a quadrilateral whose opposite sides are parallel and also congruent to each other.

The complete proof would be as shown below:

1. ABCD is a parallelogram [given]

2. AB║CD [Definition of parallelogram]

3. ∠1 ≅ ∠2, ∠3 ≅ ∠4 [alternate interior angles theorem]

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Use the limit theorem and the properties of limits to find the limit.<br> Picture provided below
sashaice [31]

Answer:

b. 1/2

Step-by-step explanation:

lim        (x -3)(x +2)

x-->-∞    ---------------

              2x^2 + x +1

= lim        (x^2 -3x +2x - 6)

x-->-∞    -----------------------

              2x^2 + x +1

= lim        (x^2 -x - 6)

x-->-∞    -----------------------

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When we plug in x = -∞, we get indeterminate form.

Now we have to use the L'hospital rule.

d/dx (x^2 - x - 6) = 2x -1

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Now apply the limit

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x--->-∞

Here we have to degree of the numerator and the denominator of the same. In this case, if x --> -∞, we get the result as the coefficient of the leading term as the result.

According to the rule, we get

= 2/4

Which can simplified as 1/2

The answer is 1/2

Hope this will helpful.

Thank you.

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