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taurus [48]
3 years ago
7

Can someone please check to make sure I got this correct? I would appreciate if you showed your work so that I could compare wit

h my work. Thank you!

Mathematics
1 answer:
dmitriy555 [2]3 years ago
8 0

Answer:

-4

Step-by-step explanation:

[√2(cos(3π/4) + i sin(3π/4))]⁴

(√2)⁴ (cos(3π/4) + i sin(3π/4))⁴

4 (cos(3π/4) + i sin(3π/4))⁴

Using De Moivre's Theorem:

4 (cos(4 × 3π/4) + i sin(4 × 3π/4))

4 (cos(3π) + i sin(3π))

3π on the unit circle is the same as π:

4 (cos(π) + i sin(π))

4 (-1 + i (0))

-4

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We conclude that all the points of the table satisfy the equation y = x²

Hence, the option containing the equation y =  x² is true.

The graph of y =  x² is also attached below.

Step-by-step explanation:

Given the table

x             y

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-1             1

0            0

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y = x²

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y = (-2)² = 4

so the point (2, 4) lies on the graph of y =  x²

y = x²

plun in x = -1

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so the point (-1, 1) lies on the graph of y =  x²

y = x²

plun in x = 0

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so the point (0, 0) lies on the graph of y =  x²

y = x²

plun in x = 1

y = (1)² = 1

so the point (1, 1) lies on the graph of y =  x²

y = x²

plun in x = 2

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so the point (2, 4) lies on the graph of y =  x²

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The graph of y =  x² is also attached below.

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