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2 years ago

Simplify (10 + 3i)(5 − 2i).

Mathematics

2 answers:

Romashka [77]2 years ago

6 0

The answer I think is D but use the app photo math very useful:)

kirza4 [7]2 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 number 4 is the smallest positive integer that has exactly three factors: 1, 2, and 4. If k is the next-highest integer that

saul85 [17]

To solve this problem, we must do a method of trial and error to find for the next highest integer with exactly three factors. We know that the value of k must be greater than 4, therefore by using trial and error to find for the correct answer:

Factors of 5:1, 5

Factors of 6:1, 2, 3, 6

Factors of 7:1, 7

Factors of 8:1, 2, 4, 8

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The sum of the factors is:

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2 years ago

If the diagonal of a square is approximately 12.73, what is the length of its sides?

Alja [10]

Answer:

The length of the sides of the square is 9.0015

Step-by-step explanation:

Given

The diagonal of a square = 12.73

Required

The length of its side

Let the length and the diagonal of the square be represented by L and D, respectively.

So that

D = 12.73

The relationship between the diagonal and the length of a square is given by the Pythagoras theorem as follows:

$D^{2} = L^{2} + L^{2}$

Solving further, we have

$D^{2} = 2L^{2}$

Divide both sides by 2

$\frac{D^{2}}{2} = \frac{2L^{2}}{2}$

$\frac{D^{2}}{2} = L^2$

Take Square root of both sides

$\sqrt{\frac{D^{2}}{2}} = \sqrt{L^2}$

$\sqrt{\frac{D^{2}}{2}} = L$

Reorder

$L = \sqrt{\frac{D^{2}}{2}}$

Now, the value of L can be calculated by substituting 12.73 for D

$L = \sqrt{\frac{12.73^{2}}{2}}$

$L = \sqrt{\frac{162.0529}{2}}$

$L = \sqrt{{81.02645}$

$L = 9.001469325$

$L = 9.0015$ (Approximated)

Hence, the length of the sides of the square is approximately 9.0015

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