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3 years ago

Explain how to multiply the complex #'s (3+2i)(4-i)

1 answer:

8 0

Multiply the numbers like you multiply binomials.
Multiply every term of the first binomial by every term of the second binomial.
Then combine like terms, and remember that i^2 = -1.

(3 + 2i)(4 - i) =

= 12 - 3i + 8i - 2i^2

= 12 + 5i + 2

= 14 + 5i

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Monica asked her friends to buy a charity raffle ticket for $3. All but 4 of her friends bought a ticket, and she raised $18. Ho

jok3333 [9.3K]

Answer:

10 friends

Step-by-step explanation:

$18/$3 = 6

6 = number of friends that bought a ticket.

4 = number of friends who didn't buy a ticket.

end result, 6+4 = 10

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3 years ago

Where would 2.25 be plotted on the number line

lawyer [7]

2.25 is 2 1/4

so 1/4 between 2 and 3 on the number line

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4 years ago

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alina1380 [7]

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3 years ago

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Please answer that question

german

The polar form of the complex numbers are z₁ = 6 · $e^{i\,\frac{11\pi}{6} }$ and z₂ = √2 · $e^{i\,\frac{3\pi}{4} }$ . The multiplication of the numbers is z₁ · z₂ = 6√2 · $e^{i\,\frac{31\pi}{12} }$ , the division of the numbers is z₁ / z₂ = 3√2 · $e^{i\,\frac{13\pi}{12} }$ and the reciprocal of a number is 1 / z₁ = (1 / 6) · $e^{-i\,\frac{11\pi}{6} }$ .

<h3>How to find complex numbers in polar forms and make operations with them </h3>

In this problem we find two complex numbers in rectangular form (z = a + i b), whose polar form has to be found. The complex form is described below:

z = r · $e^{i\,\theta}$

Where:

r - Norm
θ - Direction, in radians.

The magnitude is determined by Pythagorean theorem:

r = √(a² + b²)

And the direction by inverse trigonometric functions:

θ = tan⁻¹ (b / a)

Polar form offers a quicker manner to perform multiplication and division of complex numbers. Thus:

Multiplication

z₁ · z₂ = r₁ · r₂ · $e^{i\,(\theta_1 + \theta_2)}$

Division

z₁ / z₂ = (r₁ / r₂) · $e^{i\,\frac{\theta_{1}}{\theta_{2}} }$

First, determine the magnitudes of each complex number:

r₁ = √[(3√3)² + (- 3)²]

r₁ = 6

r₂ = √[(- 1)² + 1²]

r₂ = √2

Second, determine the directions of each complex number:

θ₁ = 11π / 6

θ₂ = 3π / 4

Third, write the complex numbers in polar form:

z₁ = 6 · $e^{i\,\frac{11\pi}{6} }$

z₂ = √2 · $e^{i\,\frac{3\pi}{4} }$

Fourth, find the multiplication of the complex numbers:

z₁ · z₂ = 6√2 · $e^{i\,\frac{31\pi}{12} }$

Fifth, find the division of the complex numbers:

z₁ / z₂ = 3√2 · $e^{i\,\frac{13\pi}{12} }$

Sixth, find the reciprocal of the complex number:

1 / z₁ = (1 / 6) · $e^{-i\,\frac{11\pi}{6} }$

To learn more on complex numbers: brainly.com/question/20566728

#SPJ1

6 0

1 year ago

Can you help please

AysviL [449]

Answer:

The last two options.

Step-by-step explanation:

y=2x+4 (replace the x with 1) y=2(1)+4 Y=6

y= 2x+4 replace the x with 2) y= 2(2)+4 Y= 8

So the y coordinate can be 6 or 8.

(x,y)

ANSWER: (1,6) and (2,8)

HOPE THIS HELPS!!!

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3 years ago

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