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

\frac{4 ^{x}}{2 ^{x}}

\frac{2}{4} + \frac{2}{6} + \frac{1}{8}

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

- 7160 + 40