Possible ordered pair(s) (x,y) on the complex plane satisfying the relation (4 - 31)/2 + (3 + 21xy = 472 - (3xy – 2yzji is/are – (4-3) 0 (-22) (6,9) (10,15)
Answers
Given : (4 - 3i)x² + (3 + 2i)xy = 4y² - x²/2 + (3xy – 2y²)i
To Find : Possible ordered pair(s)
(4,-3)
(-2,2)
(6,9)
(10,15)
Solution:
(4 - 3i)x² + (3 + 2i)xy = 4y² - x²/2 + (3xy – 2y²)i
=> 4x² - 3x²i + 3xy + 2xyi = 4y² - x²/2 + 3xyi - 2y²i
=> 4x² + x²/2 - 4y² + 3xy + i(-3x² + 2xy - 3xy + 2y²) = 0
=> (9x²/2 - 4y² + 3xy ) + i(-3x² + 2y² - xy ) = 0
9x²/2 - 4y² + 3xy = 0
=> 9x² - 8y² + 6xy = 0 Eq1
-3x² + 2y² - xy = 0 Eq2
Eq1 + 6 * Eq2
=> -9x² + 4y² = 0
=> 4y² = 9x²
=> y = ±3x/2
Eq1 + 3 * Eq2
=> -2y² + 3xy = 0
=> y(-2y + 3x) = 0
=> y = 0 and y = 3x/2
Eq1 + 4 * Eq2
-3x² + 2xy = 0
=> -x(3x - 2y) = 9
=> x= 0 or y = 3x/2
y = 3x/2
x = 4 => y = 6
x = - 2 => y = - 3
x = 6 => y = 9
x = 10 => y = 15
Hence ( 6 , 9) and ( 10 , 15) ordered pair(s) satisfy the relation
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