1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mariarad [96]
3 years ago
14

Simplify the following expression into the form a + bi, where a and b are rational numbers.

Mathematics
2 answers:
vagabundo [1.1K]3 years ago
7 0
The answer is -16 - 10i.

Using the distributive property on the first part, we have:
-2i*7--2i*4i + (3+i)(-2+2i)
-14i+8i² +(3+i)(-2+2i)

Using FOIL on the last part,
-14i+8i²+(3*-2+3*2i+i*-2+i*2i)
-14i+8i²-6+6i-2i+2i²
-10i+8i²-6+2i²

Since we know that i = -1,
-10i+8(-1)-6+2(-1)
-10i-8-6-2
-16-10i
Artyom0805 [142]3 years ago
3 0

Answer:

The simplified value of the given expression is -16-10i.

Step-by-step explanation:

The given expression is

-2i(7-4i)+(3+i)(-2+2i)

We need to convert the expression into the form a + bi, where a and b are rational numbers.

Using distributive property we get

-2i(7)-2i(-4i)+3(-2+2i)+i(-2+2i)

-14i+8i^2+3(-2)+3(2i)+i(-2)+i(2i)

-14i+8i^2-6+6i-2i+2i^2

Combine like terms.

10i^2-10i+6

Substitute i^2=-1,

10(-1)-10i-6

-10-10i-6

Combine like terms.

-16-10i

Therefore the simplified value of the given expression is -16-10i.

You might be interested in
Determine whether or not the following question can be considered as a statistical question.
tensa zangetsu [6.8K]
No its not a statistical question

5 0
3 years ago
"Four times the difference of a number and<br> seven is at least -52."
dedylja [7]
Remember ‘difference’ refers to subtraction, so they are looking for the ‘difference’ of a a number, which is unknown, so we can use the variable ‘x.’ X-7

The term ‘at least’ refers to our greater than, less than, equal to signs

Difference of a number and 7 = x-7
Four times = (4) or •4
At least = <
-52 = Answer negative 52
Plug them all in,

x-7(4)<-52
7 0
2 years ago
The probability of rolling a 6 with a six-sided number cube is 1/6 Choose the
Pavel [41]

Answer:

UNLIKELY

Step-by-step explanation:

Given that:

Probability of rolling a six with a six sided nuner cube = 1/6

Required outcome / Total possible outcomes

Number of 6 / total sides of number cube = 1/6

The probability value obtained shows that there is a chance of getting a six ; however it is possible at about once in every 6 rolls of the dice.

Hence getting a six isn't impossible but the chance is small. A probability of 1/6 is the smallest that can be obtained for any of each number on the dice. Hence, it could be said that the likelihood is 'UNLIKELY'

7 0
3 years ago
Amanda bought a television that costs z dollars. She paid 20% at the store and then made 6 equal payments. Which expression repr
maxonik [38]

Explanation is in the file

tinyurl.com/wtjfavyw

5 0
3 years ago
Evaluate : <br> \(\cos 12 \cos 24 \cos 36 \cos 48 \cos 72 \cos 84\)
NeTakaya
The answer in itself is 1/128 and here is the procedure to prove it:
cos(A)*cos(60+A)*cos(60-A) = cos(A)*(cos²60 - sin²A) 

<span>= cos(A)*{(1/4) - 1 + cos²A} = cos(A)*(cos²A - 3/4) </span>

<span>= (1/4){4cos^3(A) - 3cos(A)} = (1/4)*cos(3A) </span>

Now we group applying what we see above

<span>cos(12)*cos(48)*cos(72) = </span>
<span>=cos(12)*cos(60-12)*cos(60+12) = (1/4)cos(36) </span>

<span>Similarly, cos(24)*cos(36)*cos(84) = (1/4)cos(72) </span>

<span>Now the given expression is: </span>

<span>= (1/4)cos(36)*(1/4)*cos(72)*cos(60) = </span>

<span>= (1/16)*(1/2)*{(√5 + 1)/4}*{(√5 - 1)/4} [cos(60) = 1/2; </span>
<span>cos(36) = (√5 + 1)/4 and cos(72) = cos(90-18) = </span>
<span>= sin(18) = (√5 - 1)/4] </span>
<span>And we seimplify it and it goes: (1/512)*(5-1) = 1/128</span>
4 0
3 years ago
Other questions:
  • Y=-2x+11 what is the slope and y intercept?
    14·2 answers
  • Choose the best definition for the following term:substitution
    15·2 answers
  • 2x - 5y = -6<br> -2x + 7y = 14
    5·1 answer
  • I need help(This is due in a few hours)
    11·1 answer
  • SOMEONE PLEASE HELP I NEED IT there is a lonk to see it
    6·1 answer
  • HELP PLS MIGHT GIVE BRAINLIST BUT ONLY IF 2 PEOPLE ANSWER!
    12·1 answer
  • Sam deposited $400 into her savings account that earned 4.5% interest per year. How much money did she have after 2.5 years?
    15·1 answer
  • john runs 2/5 miles in 1/20 of an hour. if he runs at a constant rate, what is his speed, in miles per hour?
    9·1 answer
  • What does point 4, 32 mean in this situation
    5·1 answer
  • A chemist makes a solution of acetic acid. The chemist makes at least 2 liters and wants to store the solution in several smalle
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!