mathematics ughh !!-_- so done wtih this math!
solve the following equations for real X and Y
1) (2-3i) (x+yi) = 4+i
2) (2-2i) (x+yi) = 2(x=2yi) + 2i - 1
need help :( after getting answer i m gonna write this mathematics in my death note lol
come on someone ahh
Btw there are teachers who help us or they are students??
1) (2-3i) (x+yi) = 4+i
is the same as
2(x+yi) -3i(x+iy) = 4 + i
2 x + 2 y i - 3 x i + 3 y = 4 + i
so
2 x + 3 y = 4
2 y - 3 x = 1
then first times 2, second times 3
4 x + 6 y = 8
6 y - 9 x = 3
----------------- subtract
13 x =5
x = 5/13
etc
Retired engineering professor
ahh cool retired engineering professor sounds so awesome
by the way thank you :) i got right answer ^_^
I understand that math can sometimes be frustrating, but don't worry, I'm here to help!
Let's start by solving the first equation, (2-3i)(x+yi) = 4+i:
To multiply two complex numbers, we use the distributive property, just like with real numbers.
Step 1: Distribute (multiply) the complex number (2-3i) into (x+yi):
(2-3i)(x+yi) = 4+i
This gives us:
2x + 2yi - 3ix - 3iy^2 = 4 + i
Notice that "i^2" is equal to -1. We can substitute this into the equation:
2x + 2yi - 3ix - 3i(-1) = 4 + i
Simplifying further:
2x + 2yi - 3ix + 3i = 4 + i
Step 2: Separate the real and imaginary parts:
(2x - 3y) + (2y + 3x)i = 4 + i
Now we have a system of equations:
2x - 3y = 4 (equation 1)
2y + 3x = 1 (equation 2)
Solving this system of linear equations will give us the values of x and y that satisfy the equation.
For the second equation, (2-2i)(x+yi) = 2(x+2yi) + 2i - 1, we can follow a similar process.
Step 1: Distribute (multiply) the complex number (2-2i) into (x+yi):
(2-2i)(x+yi) = 2(x+2yi) + 2i - 1
This gives us:
2x + 2yi - 2ix - 2iy^2 = 2x + 4yi + 2i - 1
Again, substitute i^2 with -1:
2x + 2yi - 2ix - 2i(-1) = 2x + 4yi + 2i - 1
Simplifying further:
2x + 2yi - 2ix + 2i = 2x + 4yi + 2i - 1
Step 2: Separate the real and imaginary parts:
(2x - 2y) + (2y + 2x)i = 2x + 4y + i - 1
Now we have a new system of linear equations:
2x - 2y = -1 (equation 1)
2y + 2x = 1 (equation 2)
Solving this system of linear equations will give us the values of x and y that satisfy the equation.
I hope this helps you solve the equations! Remember, practice makes perfect, and with some patience, you can overcome these challenges.