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
Sonja [21]
3 years ago
5

4. Explain what an imaginary number is and its relationship to complex numbers. Then give

Mathematics
2 answers:
SpyIntel [72]3 years ago
7 0

Answer:

564643

Step-by-step explanation:

STALIN [3.7K]3 years ago
3 0

Answer:

In the real number system, there is no solution to the equation x^2=-1x

2

=−1x, squared, equals, minus, 1. In this lesson, we will study a new number system in which the equation does have a solution.

The backbone of this new number system is the number iii, also known as the imaginary unit.

i^2=-1i

2

=−1i, squared, equals, minus, 1

\sqrt{-1}=i

−1

​

=isquare root of, minus, 1, end square root, equals, i

By taking multiples of this imaginary unit, we can create infinitely many more new numbers, like 3i3i3, i, i\sqrt{5}i

5

​

i, square root of, 5, end square root, and -12i−12iminus, 12, i. These are examples of imaginary numbers.

However, we can go even further than that and add real numbers and imaginary numbers, for example 2+7i2+7i2, plus, 7, i and 3-\sqrt{2}i3−

2

​

i3, minus, square root of, 2, end square root, i. These combinations are called complex numbers.

Defining complex numbers

A complex number is any number that can be written as \greenD{a}+\blueD{b}ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i, where iii is the imaginary unit and \greenD{a}astart color #1fab54, a, end color #1fab54 and \blueD{b}bstart color #11accd, b, end color #11accd are real numbers.

\begin{array}{ccc} \Large\greenD a&\Large+&\Large \blueD bi \\ \uparrow&&\uparrow\phantom{i} \\ \text{Real}&&\text{Imaginary} \\ \text{part}&&\text{part} \end{array}

a

↑

Real

part

​

 

+

​

 

bi

↑i

Imaginary

part

​

\greenD aastart color #1fab54, a, end color #1fab54 is called the \greenD{\text{real}}realstart color #1fab54, start text, r, e, a, l, end text, end color #1fab54 part of the number, and \blueD bbstart color #11accd, b, end color #11accd is called the \blueD{\text{imaginary}}imaginarystart color #11accd, start text, i, m, a, g, i, n, a, r, y, end text, end color #11accd part of the number.

The table below shows examples of complex numbers, with the real and imaginary parts identified. Some people find it easier to identify the real and imaginary parts if the number is written in standard form.

Complex Number Standard Form \greenD a+\blueD b ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i Description of parts

7i-27i−27, i, minus, 2 \greenD {-2}+\blueD 7i−2+7istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 7, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 77start color #11accd, 7, end color #11accd.

4-3i4−3i4, minus, 3, i \greenD 4 + (\blueD{-3})i4+(−3)istart color #1fab54, 4, end color #1fab54, plus, left parenthesis, start color #11accd, minus, 3, end color #11accd, right parenthesis, i The real part is \greenD{4}4start color #1fab54, 4, end color #1fab54 and the imaginary part is \blueD{-3}−3start color #11accd, minus, 3, end color #11accd

9i9i9, i \greenD 0+\blueD9i0+9istart color #1fab54, 0, end color #1fab54, plus, start color #11accd, 9, end color #11accd, i The real part is \greenD{0}0start color #1fab54, 0, end color #1fab54 and the imaginary part is \blueD 99start color #11accd, 9, end color #11accd

-2−2minus, 2 \greenD {-2}+\blueD0i−2+0istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 0, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 00start color #11accd, 0, end color #11accd

Step-by-step explanation:

plz brian list and allways happy to help.

You might be interested in
1. Students who attended a track and field meet were polled, and 75% of them said that track and field meets are more fun to att
IRINA_888 [86]

Answer:

Part 1: It is not a valid conclusion to say that track and field sports are more popular than soccer based on the survey. The survey was taken at a track and field event so the people that were surveyed are probably biased.

Part 2: A better way of determining which sport is more popular is by counting how many people show up to each event and comparing the results.  

6 0
3 years ago
What is n/8=11/5 solve for n<br><br><br> #youngboy comment
mihalych1998 [28]

n should be 8 according to mathmatical laws

8 0
3 years ago
Starting from the same place, Ryu walks due west and Samantha walks due east.
juin [17]

For Samantha, 2 tick marks east is 120 units east because 1 tick is 60 units.

For Ryu, 8 tick marks west is 480 units west because 1 tick is 60 units.

They are walking to form a line. Just add their distances from 0.

120 + 480 = 600.

--------------------------0----------------------------

Ryu: 480                         Samantha: 120

         480              +             120           =    600.

600 units, or feet.

5 0
3 years ago
A . expression A
yan [13]

Answer:

answer choice B.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Complete the ratio tables.<br> 10<br> 20<br> 25<br> 50<br> 60
Misha Larkins [42]

Answer:

what do u want me to do

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Really really need this answer. Please help!
    9·1 answer
  • What is the constant proportionally of y=2.5x
    11·2 answers
  • Perform indicated operations for function: f(x)=x^2+1 use in f(x+h)-f(x)/h
    8·1 answer
  • The fastest that a seahorse can travel is 2,640 feet per hour. What is its top speed in miles per hour? plz i need help
    15·2 answers
  • A construction worker has a rope that is 6 m long. She needs to cut it into pieces that are each 3/7 m long. How many such piece
    12·1 answer
  • The product of 4 and the sum of a number and 12 is more than 16
    5·1 answer
  • The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of
    7·2 answers
  • 4,11,18<br> what is the 109th value of this sequence ?
    14·1 answer
  • What would be the second step in this problem? (3 + 4) 9 + 3 =
    14·2 answers
  • Ben is studying photography, and he was asked to submit 6 photographs from his collection to exhibit at the fair. He has 15 phot
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!