F.4 Maths

(5 - 3i)/(4 + 3i) = (x + y) + (3x - y)i

Consider
LHS
= (5 - 3i)/(4 + 3i)
= (5 - 3i)/(4 + 3i) × (4 - 3i)/(4 - 3i)
= [(5 - 3i) × (4 - 3i)] / [(4 + 3i) × (4 - 3i)]
= (20 - 15i - 12i + 9i²) / [4² - (3i)²]
= (20 - 27i - 9) / (16 + 9)
= (11 - 27i) / 25
= 11/25 - (27/25)i

Therefore, consider
{ x + y = 11/25
{ 3x - y = -27/25

4x = -16/25
x = -4/25
y = 11/25 - x = 15/25 = 3/5

The answer is:
x = -4/25
y = 3/5


2014-09-14 19:14:18 補充：
噢，Leo，謝謝你～

你真有風度！

加油！

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(5 - 3i) / (4 + 3i) = (x + y) + (3x - y)i

(5 - 3i) = (4 + 3i)[(x + y) + (3x - y)i]

(5 - 3i) = 4x + 4y + 12xi - 4yi + 3xi + 3yi - 9x + 3y

(5 - 3i) = (-5x + 7y) + (15x - y)i

So,

-5x + 7y = 5, 15x - y = -3

y = 15x + 3

-5x + 7(15x + 3) = 5

100x = -16

x = -4/25

y = 15x + 3 = 3/5

迟咗几秒.搬到意見柵

(5-3i)/(4+3i) = (x+y) +(3x-y)i
(5-3i) = (4+3i)[(x+y) +(3x-y)i]
(5-3i) = [4x+4y +(12x-4y)i+(3x+3y)i +(9x-3y)i^2]
(5-3i) = [4x+4y +(15x-y)i -(9x-3y)]
(5-3i) = 7y-5x +(15x-y)i
∴
5=7y-5x ___(1)
-3=15x-y___(2)

(1)*3+(2),
12=20y
y=3/5

put y=3/5 into (2)
-3=15x-3/5
x=-4/25

∴
x=-4/25
y=3/5