What is (x-3+4i)(x-3-4i) ?

The solution to (x-3+4i)(x-3-4i) is x^2-6x+25

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simplify (x-3+4i)(x-3-4i)

simplify

(x - 3 + 4 i) (x - 3 - 4 i)

x^{2} - 6 x + 25

Solution steps

(x - 3 + 4 i) (x - 3 - 4 i)

Rewrite

x - 3 + 4 i

in standard complex form:

(x - 3) + 4 i

Rewrite

x - 3 - 4 i

in standard complex form:

(x - 3) - 4 i

= ((x - 3) + 4 i) ((x - 3) - 4 i)

Apply complex arithmetic rule:

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

= (x - 3)^{2} + 4^{2}

Simplify

(x - 3)^{2} + 4^{2} : x^{2} - 6 x + 25

= x^{2} - 6 x + 25

(- 4 + 7 i) + (- 4 - 7 i)

x y - 101 x^{2} + x^{2} - x^{2} y^{2} + 99 x y

3 x^{3} - 25 x^{2} + 58 x - 40

\frac{7}{53}

\frac{1}{4} \times (- 1)