If x and y are real numbers and if 2x+8i=3+iy find the numerical value of x?

Answer 1

Because x and y are real, we know that the real parts of each side of the equation are the same. Likewise, so are the imaginary parts. That is:

2x = 3
8i = yi

Solving for x in 2x=3 gives: x=3/2
Solving for y in 8i=yi gives: y=8

Answer 2

if xy = 18, then y = 18/x so discover the minimum of 2x + 18/x. Take the spinoff and set to 0. 2 + ( (0x - 18)/x^2) = 0 2 - 18/(x^2) = 0 -18/(x^2) = -2 2x^2 = 18 x^2 = 9 x = 3 So y = 6 the answer is (3,6) and the minimum is 12

Answer 3

Note that two complex numbers

a+ib and x+iy are equal if and only if a = x and y = b (this means that two points on the complex plane coincide)

From your statement and the fact that x and y are real numbers we get

2x = 3 and y = 8, so x = 3/2 or 1.5

Answer 4

Just equate the real parts
2x = 3
x = 3/2.
For y, y = 8.
Two complex numbers are equal if and
only if their real parts are equal and their
imaginary parts are equal.