What is (x-1+isqrt(2))^2*(x+1+isqrt(2))^2 ?

The solution to (x-1+isqrt(2))^2*(x+1+isqrt(2))^2 is (x^4-14x^2+9)+(4sqrt(2)x^3-12sqrt(2)x)i

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simplify (x-1+isqrt(2))^2*(x+1+isqrt(2))^2

simplify

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

(x^{4} - 14 x^{2} + 9) + (42 x^{3} - 122 x) i

Solution steps

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

Expand

(x - 1 + i 2)^{2} : x^{2} - 2 x - 22 i + 22 x i - 1

= (x^{2} - 2 x - 22 i + 22 x i - 1) (x + 1 + i 2)^{2}

Expand

(x + 1 + i 2)^{2} : x^{2} + 2 x + 22 i + 22 x i - 1

= (x^{2} - 2 x - 22 i + 22 x i - 1) (x^{2} + 2 x + 22 i + 22 x i - 1)

Distribute parentheses

= x^{2} x^{2} + x^{2} \cdot 2 x + x^{2} \cdot 22 i + x^{2} \cdot 22 x i + x^{2} (- 1) - 2 x x^{2} - 2 x \cdot 2 x - 2 x \cdot 22 i - 2 x \cdot 22 x i - 2 x (- 1) - 22 i x^{2} - 22 i 2 x - 22 i 22 i - 22 i 22 x i - 22 i (- 1) + 22 x i x^{2} + 22 x i 2 x + 22 x i 22 i + 22 x i 22 x i + 22 x i (- 1) - 1 \cdot x^{2} - 1 \cdot 2 x - 1 \cdot 22 i - 1 \cdot 22 x i - 1 \cdot (- 1)

Simplify

x^{2} x^{2} + x^{2} \cdot 2 x + x^{2} \cdot 22 i + x^{2} \cdot 22 x i + x^{2} (- 1) - 2 x x^{2} - 2 x \cdot 2 x - 2 x \cdot 22 i - 2 x \cdot 22 x i - 2 x (- 1) - 22 i x^{2} - 22 i 2 x - 22 i 22 i - 22 i 22 x i - 22 i (- 1) + 22 x i x^{2} + 22 x i 2 x + 22 x i 22 i + 22 x i 22 x i + 22 x i (- 1) - 1 \cdot x^{2} - 1 \cdot 2 x - 1 \cdot 22 i - 1 \cdot 22 x i - 1 \cdot (- 1) : x^{4} - 14 x^{2} + 42 x^{3} i - 122 x i + 9

= x^{4} - 14 x^{2} + 42 x^{3} i - 122 x i + 9

Rewrite in standard complex form:

(x^{4} - 14 x^{2} + 9) + (42 x^{3} - 122 x) i

= (x^{4} - 14 x^{2} + 9) + (42 x^{3} - 122 x) i

lo g_{x} (\frac{y}{3 z})

(x - 5) (x + 5)

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

\frac{( 3 x ^{4} )}{( 8 x ^{5} - 3 ) ^{4}}

2 x (1 + 2 ln (x))

What is (x-1+isqrt(2))^2*(x+1+isqrt(2))^2 ?
The solution to (x-1+isqrt(2))^2*(x+1+isqrt(2))^2 is (x^4-14x^2+9)+(4sqrt(2)x^3-12sqrt(2)x)i