What is (x-4-i)(x-4+i) ?

The solution to (x-4-i)(x-4+i) is x^2-8x+17

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simplify (x-4-i)(x-4+i)

simplify

(x - 4 - i) (x - 4 + i)

x^{2} - 8 x + 17

Solution steps

(x - 4 - i) (x - 4 + i)

Rewrite

x - 4 - i

in standard complex form:

(x - 4) - i

= ((x - 4) - i) (x - 4 + i)

Apply complex arithmetic rule:

(a + bi) (a - bi) = a^{2} + b^{2}

= (x - 4)^{2} + (- 1)^{2}

Simplify

(x - 4)^{2} + (- 1)^{2} : x^{2} - 8 x + 17

= x^{2} - 8 x + 17

(x^{2} - 8) + (3 x - 12)

1 + 4 (6 p - 9)

\frac{1}{sec ( x ) - 1} - \frac{1}{sec ( x ) + 1}

\frac{- 3}{9}

(x^{2} + 2 x y + y^{2}) (x + y)