What is (x-2-2i)(x-2+2i) ?

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

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simplify (x-2-2i)(x-2+2i)

simplify

(x - 2 - 2 i) (x - 2 + 2 i)

x^{2} - 4 x + 8

Solution steps

(x - 2 - 2 i) (x - 2 + 2 i)

Rewrite

x - 2 - 2 i

in standard complex form:

(x - 2) - 2 i

Rewrite

x - 2 + 2 i

in standard complex form:

(x - 2) + 2 i

= ((x - 2) - 2 i) ((x - 2) + 2 i)

Apply complex arithmetic rule:

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

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

Simplify

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

= x^{2} - 4 x + 8

\frac{4}{9} + \frac{5}{6} - \frac{7}{18}

\frac{3}{5} \times 40

+ 4 x^{2} - 8 x y + 3 y^{2}

\frac{15}{6}

a b^{- 1}