Question

Please HELP ME!!!


`x=1+i` is a solution to which of the following equations?

a:
`x^(2)+1=0`
b:
`x^(2) -2x+2=0`
c:
`x^(2) -2x+1=0`
d:
`x^(2) -1=0`

If you could please share you're thought process and work with me as well, so I can better understand how you found the answer. Thanks a bunch!

Answer 1

Option B

Explanation:

`\\ \sf\longmapsto x^2-2x+2=0`

`\\ \sf\longmapsto x=(-(-2)\pm√((-2)^2-4(1)(2)))/(2(1))`

`\\ \sf\longmapsto x=(2\pm√(4-8))/(2)`

`\\ \sf\longmapsto x=(2\pm√(-4))/(2)`

`\\ \sf\longmapsto x=(2\pm 2i)/(2)`

`\\ \sf\longmapsto x=1\pm i`

Verified

Answer 2

• b. x² - 2x + 2 = 0

Explanation:

Solve each to confirm answer

a.

• x² + 1 = 0
• x² = - 1
• x = √ -1
• x = i

• FALSE

b.

• x² - 2x + 2 = 0
• (x - 1)² + 1 = 0
• (x - 1)² = - 1
• x - 1 = √-1
• x - 1 = i
• x = 1 + i

• TRUE

c.

• x² - 2x + 1 = 0
• (x - 1)² = 0
• x - 1 = 0
• x = 1

• FALSE

d.

• x² - 1 = 0
• x² = 1
• x = √1
• x = ± 1

• FALSE