If x jy2 3 4j find x and y where x y elementof RSolutionj

If (x + jy)^2 = 3 + 4j, find x and y, where x, y elementof R.

Solution

j = square root of -1 i.e. (-1)^0.5

Method: Expand the power and multiply to equate the expression to the given value and compare the coeffcieints to get the solution:

Procedure:
(x+jy)² = (x+jy) ( x+jy)
multiply this like the usual algebraic multiplication, we get:
x² + xy j + xy j + y² j²
x² +2xyj + y² (-1) (since j² = (-1^0.5)^*2 = -1¹ = -1
x² - y² + (2xy) j
comparing this to the given value of 3+4j we get
x² - y² = 3 and 2xy = 4;
since 2xy = 4, y=x/2
x² - (x/2) ² = 3
3x²/4 = 3
so x² = 4 so x = +2 or x=-2;
if x=+2 then y = 2/2 = 1
if x=-2 then y = 2/-2 = -1

Answer:
Then the answer is:
1) x = 2 and y=1 or
2) x = -2 and y = -1;