What is (x+1-2i)(x+1+2i) ?

The solution to (x+1-2i)(x+1+2i) is x^2+2x+5

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simplify (x+1-2i)(x+1+2i)

simplify

(x + 1 - 2 i) (x + 1 + 2 i)

x^{2} + 2 x + 5

Solution steps

(x + 1 - 2 i) (x + 1 + 2 i)

Rewrite

x + 1 - 2 i

in standard complex form:

(x + 1) - 2 i

Rewrite

x + 1 + 2 i

in standard complex form:

(x + 1) + 2 i

= ((x + 1) - 2 i) ((x + 1) + 2 i)

Apply complex arithmetic rule:

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

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

Simplify

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

= x^{2} + 2 x + 5

5 + 2

5 x^{2} + 405

x^{4} y + x^{2} y^{5}

\frac{1}{1 + \frac{2}{3}}

\frac{10 x + 25}{2 x + 5}