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dybincka [34]
3 years ago
13

Simplify: 9i(2+3i) enter your answer, in standard form, in the box ___

Mathematics
2 answers:
harina [27]3 years ago
8 0
-54......................
Temka [501]3 years ago
4 0

Answer:

Standard form is 9(2i-3) or (-27+18i)

Step-by-step explanation:

To solve these type of question we should always keep in mind that i= √(-1)

and i² = (-1)

We have to solve the given form 9i(2+3i).

Now we start solving the question by simplifying the factors

9i(2+3i) = 18i+27i²

⇒ 18i +27(√-1)²

⇒18i +27(-1)

⇒18i-27

⇒9(2i-3)

So the simplified for is 9(2i-3) or (-27+18i)


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Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps
Firdavs [7]
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions. 

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the 

   x²y = -4 ... (I)

Condition 2: Real parts are the same

   x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

   x²y = -4 ... (I)
   x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

   y = -3 - x² ... (II)

Substituting into equation (I)

   x²y = -4 ... (I)
   x²(-3 - x²) = -4
   -3x² - x⁴ = -4
   x⁴ + 3x² - 4 = 0
   (x² + 4)(x² - 1) = 0
   (x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

   y = -3 - x² ... (II)
   y = -3 - (±1)²
   y = -3 - 1
   y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

   -3 + ix²y 
   = -3 + i(±1)²(-4)
   = -3 - 4i

   x² + y + 4i
   = (±1)² - 4 + 4i
   = 1 - 4 + 4i
   = -3 + 4i

They result in conjugates
4 0
3 years ago
Read 2 more answers
What is the equation of the line that passes through the point (8,-3) and has an undefined slope?
BARSIC [14]

Answer:

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Step-by-step explanation:

A line with "undefined" slope is a vertical line, whose equation is of the form ...

  x = constant

In order for the line to go through a point with an x-coordinate of 8, the constant must be 8.

  x = 8 . . . . . a vertical line through (8, -3)

8 0
3 years ago
Can someone pls help me I really need help in here.. PLS…
dem82 [27]

Answer:

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5 more than the sum of p and a​
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X=5+(p+a). I think thats right idk tho
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It is letter B.
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where (h,k) is the center of the circle with radius r.
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