![boomerjm](/avatars/23766.jpg)
boomerjm
24.07.2019 •
Mathematics
When is the sum of two complex numbers a real number? when is the sum of two complex numbers an imaginary number?
Solved
Show answers
More tips
- G Goods and services How to Choose the Best Publishing House for Your Children s Book: Tips and Recommendations...
- S Science and Technology When do we change our clocks?...
- A Animals and plants How to Teach Your Parrot to Talk?...
- F Family and Home How to Remove Fading from Clothes: Tips and Tricks...
- F Food and Cooking How to Make Polendwitsa at Home?...
- F Family and Home Parents or Environment: Who Has the Most Influence on a Child s Upbringing?...
- P Philosophy Unbelievable stories of encounters with otherworldly forces...
- L Leisure and Entertainment How to Choose the Perfect Gift for Men on February 23rd?...
- H Health and Medicine How to Treat Whooping Cough in Children?...
- H Health and Medicine Simple Ways to Lower Cholesterol in the Blood: Tips and Tricks...
Answers on questions: Mathematics
- M Mathematics 78 divided by 48 what is it between...
- M Mathematics What is 2.1564 rounded to the nearest cent?...
- M Mathematics 3+7x 26 me with this equaton...
- M Mathematics What is the exact volume of the cylinder 12 in and 20 in...
- M Mathematics Round 6.8449 to the nearest hundredth...
- M Mathematics 2,231.5 milligrams = ? grams a) 2.2315 g b) 223.15 g c) 22,315 g d) 0.0022315 g...
- M Mathematics 30 points! x + 1 = 2 ÷ x + 1 in the equation above, which choice is a possible value of x + 1? a) 1 - √2 b) √2 c) 2 d) 4...
- M Mathematics What is the slope of the line that passes through the given points (3,2) and (5,12)...
- M Mathematics 1.the graph of f(x) = cos (x) is transformed into a new function, g(x), by stretching it vertically by a factor of 3 and shifting it 2 units to the left. what is the...
- M Mathematics How to express cos 3x in terms of cosx...
Ответ:
w = a+bi
z = c+di
where a,b,c,d are real numbers and i = sqrt(-1)
When is w+z purely real? When there is no imaginary part at all. Adding w and z gives
w+z = (a+bi) + (c+di)
w+z = (a+c) + (bi+di)
w+z = (a+c) + (b+d)i
The imaginary part here is (b+d)i. If we set it equal to zero, then we get
(b+d)i = 0
b+d = 0
b = -d
So if b = -d, then w+z is purely real. For instance, if w = 2+3i and z = 7-3i then
w+z = (2+3i)+(7-3i) = (2+7)+(3-3)i = 9+0i = 9
The result 9 being purely real without any imaginary part.
When is w+z purely imaginary? We'll follow the same path of logic but instead of setting the imaginary part to zero, we do that to the real part
Again,
w+z = (a+bi) + (c+di)
w+z = (a+c) + (bi+di)
w+z = (a+c) + (b+d)i
Set the real part (a+c) equal to zero and solve for zero
(a+c) = 0
a+c = 0
a = -c
When a = -c, then the sum of the complex numbers is purely imaginary
Example:
w = 9+12i
z = -9-14i
w+z = (9+12i)+(-9-14i)
w+z = (9-9)+(12i-14i)
w+z = (9-9)+(12-14)i
w+z = (0)+(-2)i
w+z = -2i
which is purely imaginary (with no real parts)
Both cases are very similar: if the corresponding values are equal but opposite, then we have cancellations to go from complex to purely real or purely imaginary. Depending of course on which values you set opposite.
The exception is that if a = -c and b = -d together, then w+z = 0 is purely real
Ответ:
no and 333943094856
Step-by-step explanation:
oh and my birthdays on friday