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3 years ago

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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3 years ago

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8090 [49]

We are given with an equation in variable y and we need to solve for y . So , now let's start !!!

We are given with ;

${:\implies \quad \sf \dfrac{33}{2}+\dfrac{3y}{5}=\dfrac{7y}{10}+15}$

Take LCM on both sides :

${:\implies \quad \sf \dfrac{165+6y}{10}=\dfrac{7y+150}{10}}$

Multiplying both sides by 10 ;

${:\implies \quad \sf \cancel{10}\times \dfrac{165+6y}{\cancel{10}}=\cancel{10}\times \dfrac{7y+150}{\cancel{10}}}$

${:\implies \quad \sf 165+6y=7y+150}$

Can be further written as ;

${:\implies \quad \sf 7y+150=165+6y}$

Transposing 6y to LHS and 150 to RHS

${:\implies \quad \sf 7y-6y=165-150}$

${:\implies \quad \bf \therefore \quad \underline{\underline{y=15}}}$

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