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3 years ago

Simplify the expression (4 + 5i)(4 − 5i). 16 − 20i 16 + 20i −9 41

Mathematics

1 answer:

Alja [10]3 years ago

5 0

Answer:

Step-by-step explanation:

Simplify the following:

(5 i + 4) (-5 i + 4)

Hint: | Multiply 4 + 5 i and 4 - 5 i together using FOIL.

(4 + 5 i) (4 - 5 i) = (4) (4) + (4) (-5 i) + (5 i) (4) + (5 i) (-5 i):

4×4 + 4 (-5 i) + 5 i×4 + 5 i (-5 i)

Hint: | Multiply 4 and 4 together.

4×4 = 16:

16 - 5×4 i + 5 i×4 + 5 i (-5)×i

Hint: | Multiply 4 and -5 together.

4 (-5) = -20:

16 + -20 i + 5 i×4 + 5 i (-5)×i

Hint: | Multiply 5 and 4 together.

5×4 = 20:

16 - 20 i + 20 i + 5 i (-5)×i

Hint: | Combine products of like terms.

5 i (-5)×i = 5 i^2 (-5):

16 - 20 i + 20 i + -5×5 i^2

Hint: | Evaluate i^2.

i^2 = -1:

16 - 20 i + 20 i - 5×5×-1

Hint: | Multiply 5 and -1 together.

5 (-1) = -5:

16 - 20 i + 20 i - 5-5

Hint: | Multiply -5 and -5 together.

-5 (-5) = 25:

16 - 20 i + 20 i + 25

Hint: | Evaluate 16 - 20 i + 20 i + 25.

16 - 20 i + 20 i + 25 = 41:

Answer: 41

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Step-by-step explanation:

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we get this by imagining a right-angled triangle inside the pyramid :

one leg is the inner height of the pyramid.

the second leg is the connection on the bottom square from the base of the inner height to the middle point of a sideline). this is half the length of a sideline.

and the baseline (Hypotenuse) is the slant height of the pyramid.

we can use Pythagoras

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with c being the Hypotenuse (side opposite of the 90° angle).

slant height² = 7² + (8/2)² = 49 + 4² = 49 + 16 = 65

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so, we get a areas

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Answer:

$\theta$ is in quadrant II

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$\sin(\theta) > 0$ and $\cos(\theta) < 0$

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3 years ago

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djverab [1.8K]

Answer:

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3 years ago

-16 + 5n= -7(-6 + 8n) + 3

Amiraneli [1.4K]

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$n = 1$

<h3>I hope this helps!</h3><h3>Best regards,</h3><h3>MasterInvestor</h3>

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4 years ago

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