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

The solution to (x-5)^2(x-5+2i)(x+i) is (x-5)^2((x-5)x-2)+(x-5)^2(3x-5)i

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

simplify

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

(x - 5)^{2} ((x - 5) x - 2) + (x - 5)^{2} (3 x - 5) i

Solution steps

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

Rewrite

x - 5 + 2 i

in standard complex form:

(x - 5) + 2 i

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

Apply complex arithmetic rule:

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

= (x - 5)^{2} (((x - 5) x - 2 \cdot 1) + ((x - 5) \cdot 1 + 2 x) i)

Simplify

((x - 5) x - 2 \cdot 1) + ((x - 5) \cdot 1 + 2 x) i : ((x - 5) x - 2) + (3 x - 5) i

= (x - 5)^{2} (((x - 5) x - 2) + (3 x - 5) i)

Distribute parentheses

= (x - 5)^{2} ((x - 5) x - 2) + (x - 5)^{2} (3 x - 5) i

(2 p + q) (2 p - q)

A (- 14, 11) B (10, - 9) C (- 13, - 4)

3 (1 - x^{2} - \frac{x ^{2}}{( 1 - x ^{2} ) ^{\frac{1}{2}}})

\frac{1}{2} (lo g_{10} (x) y - lo g_{10} (7))

(sin (m) - tan (m)) (cos (m) - cot (m))

What is (x-5)^2(x-5+2i)(x+i) ?
The solution to (x-5)^2(x-5+2i)(x+i) is (x-5)^2((x-5)x-2)+(x-5)^2(3x-5)i