All categories

2 years ago

Multiply the complex numbers: (1∕2 + 4i)2

2 answers:

8 0

[I'm supposing that you have to find the value of (1/ 2 + 4i)²]

Answer:

$= \frac{ - 63}{4} + 4i$

Step-by-step explanation:

we must know that

(a + b)² = a² + b² + 2ab

${( \frac{1}{2} + 4i) }^{2} = { (\frac{1}{2} })^{2} + {(4i)}^{2} + 2 . \frac{1}{2} . 4i$

$= \frac{1}{4} + 16 {i}^{2} + 4i$

since i²= -1

$= \frac{1}{4} - 16 + 4i$

$= \frac{1 - 64}{4} + 4i$

$= \underline{ \frac{ - 63}{4} + 4i}$

[I'm also assuming that instead of -153/4 + 4i option A says -63/ 4 + 4i.]

so the answer is option A.

andrezito [222]2 years ago

3 0

Step-by-step explanation:

153∕4 + 8i is the correct answer

You might be interested in

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

Norma-Jean [14]

The positions when the particle reverses direction are:

$s(t_1)=55ft\\\\s(t_2)=28ft$

The acceleraton of the paticle when reverses direction is:

$a(t_1)=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=18\frac{ft}{s^{2}}$

Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

Also, when the particle reverses its direction, the velocity is equal to 0.

We are given the following function:

$s(t)=2t^{3}-21t^{2}+60t+3$

So,

- Derivating to get the velocity function, we have:

$v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60$

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

$v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s$

We know that the particle reversed its direction two times.

- Derivating the velocity function to find the acceleration function, we have:

$a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42$

Now, substituting the times to calculate the accelerations, we have:

$a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}$

Now, substitutitng the times to calculate the positions, we have:

$s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft$

Have a nice day!

3 0

2 years ago

2 R congruence theorem

Gnoma [55]

Answer:

ghj

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the degree of the following polynomial: . 3x3 + 2x - 4

klio [65]

Answer:

Step-by-step explanation:

look for the greatest exponent

5 0

2 years ago

Why is 3/2 equal to 3/4

sleet_krkn [62]

Answer:

Step-by-step explanation:

the both eual out to the same equation like how 3/4 equals 0.75 and 3/2 equals 1.5 well if you keep dividing sooner or later they will both be equal at the same number.

7 0

2 years ago

Read 2 more answers

16. [-12 Points]

Cerrena [4.2K]

Answer:

Answer: A. 5:4 Step-by-step explanation: Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 16. So the ratio is 20:16 which is simplified to = 20 and Remaining 5:4.

8 0

2 years ago