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

The solution to expand (x-i)^2(x-1+i)^2 is (x^4-2x^3-2x+3x^2)+(2+2x^2-2x)i

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

expand

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

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

Solution steps

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

Expand

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

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

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

Apply the distributive law:

m (a + b + c) = ma + mb + m c

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

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

Simplify

(x - 1 + i)^{2} x^{2} + (x - 1 + i)^{2} (- 2 x i) + (x - 1 + i)^{2} (- 1) : 2 i + x^{4} - 2 x^{3} + 2 x^{2} i - 2 x + 3 x^{2} - 2 x i

= 2 i + x^{4} - 2 x^{3} + 2 x^{2} i - 2 x + 3 x^{2} - 2 x i

Rewrite in standard complex form:

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

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

(x - 2 i) (x + 2 i) (x - 3 - i) (x - 3 + i)

2 (cot (x) - tan (x)) sin (2 x)

\frac{x ( x - 11 ) ^{2}}{( x + 6 ) ^{3}}

ln (3) (14 - x)

3 (4 x + 3 y = 8)

What is expand (x-i)^2(x-1+i)^2 ?
The solution to expand (x-i)^2(x-1+i)^2 is (x^4-2x^3-2x+3x^2)+(2+2x^2-2x)i