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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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