If c is a real number and if 1 + i is a solution of the equation x^2 -2x + c = 0, what is the value of c?
2 answers:
Answer:
c = 2
Step-by-step explanation:
Substitute x = 1 + i into the equation
(1 + i)² - 2(1 + i) + c = 0 ← distribute left side
1 + 2i + i² - 2 - 2i + c = 0 ( note that i² = - 1 )
1 + 2i - 1 - 2 - 2i + c = 0 ← collect like terms on left
- 2 + c = 0 ( add 2 to both sides )
c = 2
Answer:
c = 2.
Step-by-step explanation:
Complex solutions come in conjugate pairs so the other solution is 1 - i.
So we have:
(x - (1 + i)(x - (1 - i) = 0
(x - 1 - i)(x - 1 + i) = 0
x^2 - x + ix - x + 1 - i -ix +i - i^2 = 0
x^2 -2x + 1 - i^2 = 0
x^2 - 2x + 1 + 1 = 0
x^2 - 2x + 2 = 0
c = 2.
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r = 4.908
Step-by-step explanation:
V = 885
height (given in the picture) = 11.7
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