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Jet001 [13]
3 years ago
8

What is the product of the complex numbers 3 - 4iand 6+i where i= -1

Mathematics
2 answers:
Nadusha1986 [10]3 years ago
8 0

Answer:

Step-by-step explanation:

(3-4 \iota)(6+\iota)\\=18+3 \iota-24 \iota-4 \iota^2\\=18-21 \iota+4\\=22-21 \iota

mixas84 [53]3 years ago
5 0

Answer:

35

Step-by-step explanation:

Since i=-1, we can rewrite the equation as 3-[4(-1)} multiplied by 6+(-1). Since

4 x-1=, 3-(-4)=7. 6-1=5, and 7x5=35.

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Solve the equation by factoring: x^2-8x+15=0
blsea [12.9K]

Answer:

that is your solution

hope it helps

4 0
3 years ago
find the angle between the vectors. (first find the exact expression and then approximate to the nearest degree. ) a=[1,2,-2]. B
SashulF [63]

Answer:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

a=[1,2,-2], b=[4,0,-3,]

The dot product on this case is:

a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10

Since the dot product is not equal to zero then the two vectors are not orthogonal.

Now we can calculate the magnitude of each vector like this:

|a|= \sqrt{(1)^2 +(2)^2 +(-2)^2}=\sqrt{9} =3

|b| =\sqrt{(4)^2 +(0)^2 +(-3)^2}=\sqrt{25}= 5

And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{ab}{|a| |b|}

And the angle is given by:

\theta = cos^{-1} (\frac{ab}{|a| |b|})

If we replace we got:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

3 0
3 years ago
Find the midpoint of the segment with the following endpoints (-10,-1) and (-6,7)
Gala2k [10]

Answer:

(-8 , 3)

Step-by-step explanation:

(x1 , y1)   (x2 , y2) = (-10 , -1) (-6 , 7)

\frac{-6-10}{2} ,  \frac{7-1}{2}   -6 is going to be my x1 and -10 my y1

                     7 is going to be my x2 and -1 my y2

(-8 , 3)

7 0
3 years ago
1.) Which domain restrictions apply to the rational expression? 14x-2x / x^2-7x
mezya [45]

Answer:

3. \displaystyle 1\frac{1}{3} = x

2<em>C.</em> \displaystyle III.

2<em>B.</em> \displaystyle I.

2<em>A.</em> \displaystyle II.

1. \displaystyle Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)

Step-by-step explanation:

3. <em>See</em><em> </em><em>above</em>.

2<em>C</em>. The keyword is ratio, which signifies division, so you would choose "III.".

2<em>B</em>. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".

2<em>A</em>. The keyword is total, which signifies addition, so you would choose "II.".

1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:

\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)

I am joyous to assist you anytime.

5 0
3 years ago
Melissa has a choice of two phone plans
harina [27]
What are the plans?
( Sorry if not answering real question.)
4 0
3 years ago
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