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

The solution to (x-2-i)(x-2+i) is x^2-4x+5

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

simplify

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

x^{2} - 4 x + 5

Solution steps

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

Rewrite

x - 2 - i

in standard complex form:

(x - 2) - i

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

Apply complex arithmetic rule:

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

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

Simplify

(x - 2)^{2} + (- 1)^{2} : x^{2} - 4 x + 5

= x^{2} - 4 x + 5

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

\frac{8 x y}{( \frac{2 x}{3} \cdot \frac{2 x}{5 y} )}

- 3 (x - 4) = - 3

13 + 5 x \leq 30

x < 4 or x \geq - 1