What is (x-2+3i)(x-2-3i) ?

The solution to (x-2+3i)(x-2-3i) is x^2-4x+13

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simplify (x-2+3i)(x-2-3i)

simplify

(x - 2 + 3 i) (x - 2 - 3 i)

x^{2} - 4 x + 13

Solution steps

(x - 2 + 3 i) (x - 2 - 3 i)

Rewrite

x - 2 + 3 i

in standard complex form:

(x - 2) + 3 i

Rewrite

x - 2 - 3 i

in standard complex form:

(x - 2) - 3 i

= ((x - 2) + 3 i) ((x - 2) - 3 i)

Apply complex arithmetic rule:

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

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

Simplify

(x - 2)^{2} + 3^{2} : x^{2} - 4 x + 13

= x^{2} - 4 x + 13

\frac{2}{3} - 3

y^{2} + 2 y - 24

4 y - 6 y + 9 y = - 2

2 5^{\frac{3}{2}} + 1 6^{\frac{3}{2}}

r^{2} + 4 r + 4 = 0