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3 years ago

Which complex number does NOT fall within the shaded region in this graph?

Mathematics

1 answer:

avanturin [10]3 years ago

4 0

In order to find which is the answer, we will go step-by-step. Numbers that are not followed by I are drawn on the Real Axis and the other ones are drawn on the Imaginary Axis. You go first on the Real Axis and then on the Imaginary Axis and intersect those 2 points. If a number does not have an imaginary or real part you can assume that is equal to 0. As you can notice the number that is not in the shaded area is 2 − I

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A+5b-c=-20 4a-5b+4c=19 -a-5b-5c=2 Solve for a b and c

ludmilkaskok [199]

Answer:a = - 2

b = - 3

c = 3

Step-by-step explanation:

a + 5b - c = - 20 - - - - - - - - - 1

4a - 5b + 4c = 19 - - - - - - - - - 2

-a - 5b - 5c = 2 - - - - - - - - - - - 3

Adding equation 1 and equation 2, it becomes

- 6c = - 18

c = - 18/ - 6 = 3

Multiplying equation 2 by 1 and equation 3 by 4, it becomes

4a - 5b + 4c = 19

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Adding both equations, it becomes

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- 25b = 27 + 16c = 27 + 16 × 3

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Substituting b = - 3 and c = 3 into equation 1, it becomes

a + 5 × - 3 - 3 = - 20

a - 15 - 3 = - 20

a - 18 = - 20

a = - 20 + 18 = - 2

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