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2 years ago

Find the three cube roots of the complex number 8i. Give your answers in the form x + iy

1 answer:

5 0

8i is:
z = 8(cos(90) + i sin(90)) ; now take the 1/3 power of it.

When we take this to a normal integer power of 3 we get:

z^3 = 8^3(cos(90*3) + i sin(90*3)) right? its the same for rational exponents as well.

z^(1/3) - 2(cos(90/3) + i sin(90/3))

90/3 = 30; the cos(30)=sqrt(3)/2 and the sin(30) = 1/2 2(sqrt(3)/2 + i 1/2) = sqrt(3) + 1i should be one of the cube roots.

(sqrt(3) + i)^2 = 2 +2sqrt(3) i
(sqrt(3)+i) (2 +2sqrt(3)i
2sqrt(3) + 6i +2i -2sqrt(3) = 8i

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2 years ago

There are some monkeys in the zoo. 60% are young monkeys and the remaining are baby and old monkeys. The ratio of baby monkeys t

USPshnik [31]

Answer:

There are 60 monkeys in the Zoo

Step-by-step explanation:

In this question, we are asked to calculate the number of monkeys in a Zoo given some information to use.

Let’s have the total number of monkeys be m.

60% are going monkeys. This means number of young monkeys is 0.6m.

The number of baby and old monkeys is obviously 0.4m.

Ratio of baby to old monkeys is 3:1. This means if we splitter 0.4m into 4, number of baby monkeys is 0.3m while number of old monkeys is 0.1m

Now, subtracting the number of baby monkeys from young monkeys give a total of 18 monkeys.

Let’s project this mathematically;

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I’d be more than happy to help you if you could give me the graph

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Vladimir79 [104]

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