Eric Nicholas K's answer to lim's Junior College 2 H3 Maths Singapore question.
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I am only capable of doing this one part. Forgot my complex numbers fully.
Date Posted:
4 years ago
thanks for yout hard effort，really appreciate
Shorter alternative:
a² + b² + c² = bc + ca + ab
(-4 + 4i)² + (4 - 2i)² + c² = (4 - 2i)c + c(-4 + 4i) + (-4 + 4i)(4 - 2i)
16 - 32i - 16 + 16 - 16i - 4 + c² = c(4 - 2i - 4 + 4i) - 16 + 8i + 16i + 8
12 - 48i + c² = 2ci - 8 + 24i
c² - 2ci - 1 = 72i - 21
c² - 2ci + i² = 3(9 - 24i - 16)
(c - i)² = 3(3² - 2(3)(4i) + (4i)²)
(c - i)² = 3(3 + 4i)²
k = 3
a² + b² + c² = bc + ca + ab
(-4 + 4i)² + (4 - 2i)² + c² = (4 - 2i)c + c(-4 + 4i) + (-4 + 4i)(4 - 2i)
16 - 32i - 16 + 16 - 16i - 4 + c² = c(4 - 2i - 4 + 4i) - 16 + 8i + 16i + 8
12 - 48i + c² = 2ci - 8 + 24i
c² - 2ci - 1 = 72i - 21
c² - 2ci + i² = 3(9 - 24i - 16)
(c - i)² = 3(3² - 2(3)(4i) + (4i)²)
(c - i)² = 3(3 + 4i)²
k = 3
thanks for your alternative method
Welcome. Do take note of the need to reject the value of c with both real and imaginary part negative in the last part
deeply appreciate
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