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
saul85 [17]
1 year ago
5

Let $a$ and $b$ be nonzero real numbers such that

Mathematics
1 answer:
algol [13]1 year ago
4 0
<h3>Answer:   -7/2</h3>

=========================================================

Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7b(-1)

(2 - 7i)(a + bi) = 2a + 2bi - 7ai + 7b

(2 - 7i)(a + bi) = (2a+7b) + (2bi-7ai)

(2 - 7i)(a + bi) = (2a+7b) + (2b-7a)i

We're told the result is purely imaginary. What this means is that the real part (2a+7b) is zero, while the imaginary part (2b-7a) is nonzero. If both are zero, then we have 0+0i = 0 which is purely real.

For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

2a = -7b

a = -7b/2

a/b = -7/2 which is the final answer

We must check to see if 2b-7a is nonzero

2b - 7a = 2b - 7(-7b/2)

2b - 7a = 2b + 24.5b

2b - 7a = 26.5b

The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

------------------

A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

You might be interested in
How many rectangular prisms 8 inches long, 5 inches wide, and 2 inches high can fit into another rectangular prism that measures
tangare [24]

Answer:

20

Step-by-step explanation:

Volume of rectangular prism = length × width × height

Length = 8 inches

Width = 5 inches

Height = 2 inches

Volume of rectanglular prism = length × width × height

= 8 inches * 5 inches * 2 inches

= 80 inches ³

Dimensions of another rectangular prism:

Length = 16 inches

Width = 10 inches

Height = 10 inches

Volume of rectangular prism B = length × width × height

= 16 inches * 10 inches * 10 inches

= 1,600 inches ³

Number of prism A that fits into prism B = Volume of prism B ÷ volume of prism A

= 1,600 inches ³ ÷ 80 inches ³

= 20

Number of prism A that fits into prism B = 20

8 0
2 years ago
PLEASE HELP URGENT WILL MARK BRAINIEST
Kay [80]

Answer

DFE and FED

Step-by-step explanation:

4 0
3 years ago
Please answer a and b, I will give brainliest!!!!!
aniked [119]

Answer:

b

Step-by-step explanation:

because it passes the vertical line test and A does not if you look at x = 1 there are 2 points along that point (1,3) (1,-1)

5 0
2 years ago
Solve each quadratic equation. Show your work 15. x2 + 3x = 10
OLEGan [10]
X² + 3x = 10

Convert to standard form.
x² + 3x - 10 = 0

factor x² = x * x
factor -10 = 5 * -2

(x + 5) (x - 2) = 0
x(x -2) + 5(x-2) = 0
x² - 2x + 5x - 10 = 0
x² + 3x - 10 = 0

x + 5 = 0               x² + 3x = 10
x = -5               -5² + 3(-5) = 10
                              25 - 15 = 10
                                     10 = 10

x - 2 = 0            x² + 3x = 10
x = 2               2² + 3(2) = 10
                             4 + 6 = 10
                                 10 = 10
4 0
3 years ago
Read 2 more answers
Measures of minor arcs equal measures of inscribed angles.<br> true or false?
Vikki [24]
The answer to your question is TRUE
8 0
2 years ago
Read 2 more answers
Other questions:
  • Write 14 in scientific notation
    12·1 answer
  • What 18x+90=180 i have to solve like a equation
    13·2 answers
  • The sum of the interior angles of Michael’s polygon equals 180°. The sum of the interior angles of Cary’s polygon equals 360°. H
    7·1 answer
  • A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to
    12·1 answer
  • Anyone ?? Please urgent
    15·1 answer
  • Johnson's Nursery has net income of $42,500, depreciation expense of $1,800, interest expense of $900, taxes of $1,600, addition
    5·1 answer
  • Can anybody help me with this
    9·1 answer
  • What is the difference between -6 and -3 on a number line?
    5·2 answers
  • A coin is flipped 10 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.
    14·2 answers
  • Divide. Assume that all variables in the denominator are nonzero.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!