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
Ne4ueva [31]
3 years ago
8

A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).

Mathematics
2 answers:
Novosadov [1.4K]3 years ago
8 0
(a+bi)(2+3i)-i=(-11+5i)(1-i)
2a+3ai+2bi+3bi²-i=-11+11i+5i-5i²
2a+(3a+2b-1)i-3b=-11+16i+5
(2a-3b)+(3a+2b-1)i=-6+16i
Therefore; we have the next system of equations:
2a-3b=-6
3a+2b-1=16

Finally, the system of equations is:
2a-3b=-6
3a+2b=17
We can solve this system of equations by reduction method
 2(2a-3b=-6) 
 3(3a+2b=17)
----------------------
   13a=39  ⇒a=39/13=3

 3(2a-3b=-6)
-2(3a+2b=17)
----------------------
       -13b=-52   ⇒ b=52/13=4

Answer: a=3;    b=4

Ksivusya [100]3 years ago
8 0
<h2>Answer:</h2>

Hence, we have:

               a= 3 and b= 4

<h2>Step-by-step explanation:</h2>

It is given that:

A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).

i.e.

(a+ib)(2+3i)-i=(-11+5i)(1-i)\\\\i.e.\\\\a(2+3i)+ib(2+3i)-i=-11(1-i)+5i(1-i)\\\\i.e.\\\\2a+3ai+2bi+3bi^2-i=-11+11i+5i-5i^2

Since, we know that :

i^2=-1

Hence, we have:

2a+3ai+2bi-3b-i=-11+11i+5i+5\\\\i.e.\\\\(2a-3b)+i(3a+2b-1)=-11+5+11i+5i\\\\i.e.\\\\(2a-3b)+i(3a+2b-1)=-6+16i

i.e. we have:

2a-3b=-6---------(1)

and

3a+2b-1=16\\\\i.e.\\\\3a+2b=16+1\\\\i.e.\\\\3a+2b=17------------(2)

On multiplying equation (1) by 2 and equation (2) by 3 we get:

13a=39\\\\i.e.\\\\a=3

on putting the value of a into equation (1) we get:

2\times 3-3b=-6\\\\i.e.\\\\6-3b=-6\\\\i.e.\\\\-3b=-6-6\\\\i.e.\\\\-3b=-12\\\\i.e.\\\\b=4

You might be interested in
Use a proportion to solve the problem. Round to the nearest tenth as needed. A triangle drawn on a map has sides of lengths 9 cm
Volgvan
X/15=101/9
x= 505/3
x= 168.3 
8 0
2 years ago
The distance from a point on the number line to zero is known as:
Nana76 [90]

b. absolute value

Hope this helps!

5 0
2 years ago
Read 2 more answers
Solve the equation by the Quadratic Formula. Round to the nearest tenth, if necessary. Write your solutions from least to greate
Marat540 [252]

I hope the choices for the numerators of the solutions are given.

I am showing the complete work to find the solutions of this equation , it will help you to find an answer of your question based on this solution.

The standard form of a quadratic equation is :

ax² + bx + c = 0

And the quadratic formula is:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

So, first step is to compare the given equation with the above equation to get the value of a, b and c.

So, a = 10, b = -19 and c = 6.

Next step is to plug in these values in the above formula. Therefore,

So,

So,

Hope this helps you!

3 0
2 years ago
Which instruments listed below are examples of the classification idiophone?
rjkz [21]
Idiophone means an instrument that will produce a sound when being struck.
so the answer is B.
4 0
2 years ago
Read 2 more answers
-4.64/(-0.725) how to solve
rusak2 [61]
6.4 is the answer hope this helps
5 0
3 years ago
Read 2 more answers
Other questions:
  • Solve the following 5x - 4=2x + 8
    5·2 answers
  • Which is the atomic arithmetic sequence
    8·1 answer
  • What is the mean of the data set? 12, 17, 16, 10, 20, 13, 14, 14, 12, 12, 19, 18 a.14.75 b.15.75 c.13.50 d.14.00 need answer asa
    5·1 answer
  • I bought one more pound of apples than i did bananas. Apples cost $3.40/lb and bananas cost $2.30/lb. My total cost was $31.90.
    14·1 answer
  • Here are 10 test scores: 50, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these scores is 76. How does removing the outlier 5
    15·1 answer
  • Solve each equation.<br> 10. 5n - 16 - 8n = -10<br> What the answer to this please
    15·2 answers
  • PLEASEEEEE HELLPLPLPLPLP
    13·2 answers
  • Model solve graphs help math experts 15 points !!
    6·1 answer
  • One–fourth of the candies in a bag of are red. If there are 24 red candies, how many candies are in the bag?
    12·2 answers
  • You saved $300 from waiting tables and $100 from babysitting this
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!