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vittoriochavez9700
19.03.2021 •
Mathematics
Prove the indicated operations.
(3-i)(4+3i)(5-2i)
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Ответ:
I hope if one of these help.
Step-by-step explanation:
(4 - 3i) + (2 + i )(5 - 2i)
=16 - 2i
If you simplify your answer will be: 16−2i
1) (3+2i)-(1-6i)
2) 4i+3-6+i-1
3) 5i(3-2i)
4) (5+3i)(2-3i)
5) (2+i)(2-i)
1) (3 + 2i) - (1 - 6i)
3 + 2i - 1 + 6i
2 + 8i
2) 4i + 3 - 6 + i - 1
5i - 3 - 1
5i - 4
3) 5i ( 3 - 2i )
15i - 10i^2
15i - 10 ( -1 )
15i + 10
4) ( 5 + 3i ) ( 2 - 3i )
10 - 15i + 6i - 9i^2
10 - 9i - 9i^2
10 - 9i - 9 ( -1 )
10 - 9i + 9
- 9i + 19
5) ( 2 + i ) ( 2 - i )
4 - 2i + 2i - i^2
4 - i^2
4 - (-1)
5
1) 2 + 8i
2) -4 + 5i
3) 10 + 15i
4) 19 - 9i
5) 5
The operations with imaginary numbers are equal to those of the real numbers considering i as a variable, but with a property that allows to simplify the expression more, that is that i squared equals -1. Taking this property into account, we solve the expressions like this:
1) (3 + 2i) - (1-6i) = 3 + 2i - 1 + 6i = 2 + 8i
2) 4i + 3-6 + i-1 = 5i - 4 = -4 + 5i
3) 5i (3-2i) = 5i*3 - 5i*2i = 15i - 10i^2 = 15i - 10(-1) = 15i + 10 = 10 + 15i
4) (5 + 3i) (2-3i) = 5*2 - 5 3i + 3i*2 - 3*3i^2 = 10 - 15i + 6i - 9i^2 = 10 - 9i - 9(-1) = 10 - 9i + 9 = 19 - 9i
5) (2 + i) (2-i) = 2*2 - 2*i + 2*i - i^2 = 4 - 2i + 2i - (-1) = 4 + 1 = 5
I hope one of these help:)
Ответ:
100
Step-by-step explanation:
This is formula fot completing the square:
(b/2)^(2)
(-20/2)^(2)
100