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

i^{1389}

\frac{51}{60}

- 1^{\frac{6}{7}}

816

a^{3} \cdot (a^{3})^{2}