1.

Solve: `x^2-(7-i)x+(18-i)=0ov e rCdot`

Answer» `x^2 - (7-i)x - (18-i) = 0`
This is a quadratic equation and its roots can be given as,
`x = (-b+-sqrt(b^2-4ac))/(2a)`
Here, `a = 1, b = -(7-i), c= (18-i)`
Now, `b^2-4ac = (-(7-i))^2 - 4(18-i)`
`= 49+i^2 - 14i -72+4i`...[As `i^2 = -1`]
`= 49-1 - 14i -72+4i`
`=-24-10i`
`=1 - 25 - 2(1)(5i)`
`=1 + 25i^2 - 2(1)(5i)`
`= 1^2 + (5i)^2 - 2(1)(5i)`
`=(1-5i)^2`
`:. sqrt(b^2-4ac) = 1-5i`
`:. x = (7-i+-(1-5i))/2`
`=>x = (8-6i)/2 and x = (6-4i)/2`
`=> x = 4-3i and x = 3-2i`, which are the required solutions for the given equation.


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