飛航模式

標題:

complex number

發問:

(x+y)+(3x-y)i=(5-3i)/(4+3i) find the values of x and y.

最佳解答:

(x+y)+(3x-y)i=(5-3i)/(4+3i) find the values of x and y (5-3i)/(4+3i) = (5-3i)(4-3i)/[(4+3i)(4-3i)] = [20-15i-12i+(3i)2]/[42-(3i)2] = [20-27i+9(i)2]/[16-9(i)2] = [20-27i+9(-1)]/[16-9(-1)] = (20-27i-9)/(16+9) = (11-27i)/25 = 11/25-(27/25)i (x+y)+(3x-y)i=(5-3i)/(4+3i) (x+y)+(3x-y)i=11/25-(27/25)i x+y=11/25 . . . . . . (1) 3x-y=-27/25 . . . . . (2) (1) + (2) : 4x=-16/25 x=-4/25 Sub. x=-4/25 into (1) : y=3/5

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