What is (x+2+2i)(x+2i)(x-1+i) ?

The solution to (x+2+2i)(x+2i)(x-1+i) is (x^3+x^2-10x)+(5x^2+2x-8)i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x+2+2i)(x+2i)(x-1+i)

simplify

(x + 2 + 2 i) (x + 2 i) (x - 1 + i)

(x^{3} + x^{2} - 10 x) + (5 x^{2} + 2 x - 8) i

Solution steps

(x + 2 + 2 i) (x + 2 i) (x - 1 + i)

Rewrite

x + 2 + 2 i

in standard complex form:

(x + 2) + 2 i

= ((x + 2) + 2 i) (x + 2 i) (x - 1 + i)

Apply complex arithmetic rule:

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

= (((x + 2) x - 2 \cdot 2) + ((x + 2) \cdot 2 + 2 x) i) (x - 1 + i)

Apply complex arithmetic rule:

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

= (((x + 2) x - 2 \cdot 2) (x - 1) - ((x + 2) \cdot 2 + 2 x) \cdot 1) + (((x + 2) x - 2 \cdot 2) \cdot 1 + ((x + 2) \cdot 2 + 2 x) (x - 1)) i

Simplify

(((x + 2) x - 2 \cdot 2) (x - 1) - ((x + 2) \cdot 2 + 2 x) \cdot 1) + (((x + 2) x - 2 \cdot 2) \cdot 1 + ((x + 2) \cdot 2 + 2 x) (x - 1)) i : (x^{3} + x^{2} - 10 x) + (5 x^{2} + 2 x - 8) i

= (x^{3} + x^{2} - 10 x) + (5 x^{2} + 2 x - 8) i

sec (\frac{x}{2}) tan (\frac{x}{2}) + 2 (x - 10)^{3} + e^{5 x}

(3 + 5 i)^{5}

e^{y} (e^{- y} + 1)^{3} \frac{d y}{d x}

\frac{323 x ^{6}}{( 2 x ^{7} + 4 ) ^{3}}

What is (x+2+2i)(x+2i)(x-1+i) ?
The solution to (x+2+2i)(x+2i)(x-1+i) is (x^3+x^2-10x)+(5x^2+2x-8)i