find the values of x and y
x+5i=y+yi
To find the values of x and y in the equation x + 5i = y + yi, we can separate the real and imaginary parts.
The real part of x + 5i is x, and the imaginary part is 5i.
The real part of y + yi is y, and the imaginary part is yi.
Equating the real and imaginary parts, we have:
x = y
5i = yi
Next, we can cancel the "i" from both sides by dividing by "i":
(5i)/i = (yi)/i
5 = y
Therefore, the values of x and y are x = y = 5.
To find the values of x and y from the equation x + 5i = y + yi, we need to separate the real parts (x and y) from the imaginary parts (5i and yi) on opposite sides of the equation.
Step 1: Separate the real and imaginary parts
x + 5i = y + yi
Step 2: Combine like terms
x = y (real parts)
5i = yi (imaginary parts)
Step 3: Solve for x and y
From the real parts equation x = y, we know that the real parts of x and y are equal.
From the imaginary parts equation 5i = yi, we can cancel the common factor of i, giving us 5 = y.
Therefore, the values of x and y are x = y and y = 5.
In conclusion:
x = y
y = 5
if 5i=yi, then y is 5
and if y is 5, x=y