If the complex z = (m-1) / 3 - (m-2) I (m ∈ R), its corresponding point on the complex plane is Z, then the shortest distance from point (1,2) on the complex plane to point Z is? The answer is = 2 √ 10 / 5 | Math enthusiast | Mathematical art

If the complex z = (m-1) / 3 - (m-2) I (m ∈ R), its corresponding point on the complex plane is Z, then the shortest distance from point (1,2) on the complex plane to point Z is? The answer is = 2 √ 10 / 5

Z point coordinate is ((m-1) / 3, (m-2)) distance d ^ 2 = [(m-1) / 3-1] ^ 2 + (2 + m-2) ^ 2 = m ^ 2 / 9-8m / 9 + 16 / 9 + m ^ 2 = 10m ^ 2 / 9-8m / 9 + 16 / 9 = 2 / 9 (5m ^ 2-4m + 8) = 2 / 9 (5m ^ 2-4m + 4 / 5) + 8 / 5 = 2 / 9 (√ 5m-2 / √ 5) ^ 2 + 8 / 5, so d ^ 2 is the minimum equal to 8 / 5D, and the minimum is 2 √ 10 / 5

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