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Nutka1998 [239]
2 years ago
13

COMPLEX NUMBERS AND DEMOIVRE'S THEOREM: HELP ASAP

Mathematics
1 answer:
alisha [4.7K]2 years ago
8 0

Answer:

a = 0, b = -15

Step-by-step explanation:

Given two complex number Z1=3cispi and z2=5cis(pi/2)

In polar form;

z1 = 3(cospi + isinpi)

z1 = 3(-1+i0)

z1 = -3+0i

Z2 =  5(cospi/2 + isinpi/2)

Z2 = 5(0+i)

Z2 = 0+5i

Z1*Z2 =  (-3+0i)(0+5i)

Z1*Z2 = 0 - 15i +0i + 0i²

Z1*Z2 = 0-15i

comparing 0-15i with a + bi;

a = 0 and b = -15

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Factorize of 2a³-a²+a-2​
IrinaK [193]
<h3>Answer:  (a - 1)(2a² + a + 2)</h3>

=========================================================

Explanation:

Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2

Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.

If we tried say a = -1, then,

2a³-a²+a-2​ = 2(-1)³-(-1)²+(-1)-2​ = -6

The result is not zero, so a = -1 is not an actual root.

But if we tried say a = 1, then,

2a³-a²+a-2​ = 2(1)³-1²+1-2​ = 0

We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.

Since a = 1 is a root, this makes (a-1) to be a factor.

From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.

Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.

5 0
2 years ago
Between which 2 consecutive numbers is radical 46
Nuetrik [128]
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Answer:

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Step-by-step explanation:

Your goal is to make the second numbers, "1." So divide the first numbers by the second number to simplify.

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Answer:

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4 0
3 years ago
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