What is (x+5i-2)(x+2+5i)(x-5)^2 ?

The solution to (x+5i-2)(x+2+5i)(x-5)^2 is (x^2-29)(x-5)^2+10x(x-5)^2i

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simplify (x+5i-2)(x+2+5i)(x-5)^2

simplify

(x + 5 i - 2) (x + 2 + 5 i) (x - 5)^{2}

(x^{2} - 29) (x - 5)^{2} + 10 x (x - 5)^{2} i

Solution steps

(x + 5 i - 2) (x + 2 + 5 i) (x - 5)^{2}

Rewrite

x + 5 i - 2

in standard complex form:

(x - 2) + 5 i

Rewrite

x + 2 + 5 i

in standard complex form:

(x + 2) + 5 i

= ((x - 2) + 5 i) ((x + 2) + 5 i) (x - 5)^{2}

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= (((x - 2) (x + 2) - 5 \cdot 5) + ((x - 2) \cdot 5 + 5 (x + 2)) i) (x - 5)^{2}

Simplify

((x - 2) (x + 2) - 5 \cdot 5) + ((x - 2) \cdot 5 + 5 (x + 2)) i : (x^{2} - 29) + 10 x i

= ((x^{2} - 29) + 10 x i) (x - 5)^{2}

Distribute parentheses

= (x^{2} - 29) (x - 5)^{2} + 10 x (x - 5)^{2} i

\frac{ln ( ( y ^{2} - 1 ) ( x ^{2} - 1 ) )}{2}

(cos (θ) + i sin (θ))^{6}

\frac{d}{d v} ((p) (p + \frac{9.5}{v ^{2}}) (v - 9.8))

3 (a - \frac{1}{6})^{2} - \frac{49}{12}

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

What is (x+5i-2)(x+2+5i)(x-5)^2 ?
The solution to (x+5i-2)(x+2+5i)(x-5)^2 is (x^2-29)(x-5)^2+10x(x-5)^2i