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grigory [225]
3 years ago
12

What is the factored form of the expression over the complex numbers? 16x^2+9y^2

Mathematics
2 answers:
sertanlavr [38]3 years ago
8 0
I hope this helps you

noname [10]3 years ago
3 0

Answer: The factored form of the expression over the complex numbers is (4x+i3y)(4x-i3z)

Step-by-step explanation:

Since we have given that

16x^2+9y^2

We need to factorise the above equation.

As we know that

(a^2+b^2)=(a+ib)(a-ib)

16=4^2\\\\and\\\\9=3^2

and it can be written as

16x^2+9y^2=(4x)^2+(3y)^2=(4x+i3y)(4x-i3y)

Hence, the factored form of the expression over the complex numbers is

(4x+i3y)(4x-i3z)

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Urgent!! Will mark brainliest!!
anastassius [24]

Answer:

1) tanФ = 0.8392 ⇒ 2nd answer

2) cosФ = 20/29 ⇒ 3rd answer

3) cosФ = -√2/2 , cotФ = -1 ⇒ first answer

Step-by-step explanation:

* At first check the quadrant of the angle

∵ 180° < Ф < 270°

∴ Ф lies on the third quadrant

* Remember in the 3rd quadrant tanФ and cotФ only positive

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∵ tan²Ф = sec²Ф - 1

∵ secФ = 1/sinФ

∵ secФ = 1/-0.7660

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∴ cosФ = ± 20/29

* Because Ф lies in the 1st quadrant

∴ cosФ = 20/29

* Remember that when the point is at the terminal side of angle Ф

∴ Its x-coordinate is cosФ

∴ Its y-coordinate is sinФ

* The point is (-√2/2 , √2/2)

∵ x-coordinate is negative ad y-coordinate is positive

∴ the point is on the 2nd quadrant

∴ 90° < Ф < 180°

∴ The values of sinФ and cscФ only positive

* From previous we know that:

∴ cosФ = -√2/2

∴ sinФ = √2/2

∵ cotФ = cosФ/sinФ

∴ cotФ = -√2/2 ÷ √2/2 = -√2/2 × 2/√2 = -√2/√2 = -1

* cosФ = -√2/2 , cotФ = -1

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