What is (x-1-2i)^3(x-1+2i) ?

The solution to (x-1-2i)^3(x-1+2i) is (x^4-4x^3+6x^2-4x-15)+(20-28x+12x^2-4x^3)i

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simplify (x-1-2i)^3(x-1+2i)

simplify

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

(x^{4} - 4 x^{3} + 6 x^{2} - 4 x - 15) + (20 - 28 x + 12 x^{2} - 4 x^{3}) i

Solution steps

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

Apply the distributive law:

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

(x - 1 - 2 i)^{3} (x - 1 + 2 i) = (x - 1 - 2 i)^{3} x + (x - 1 - 2 i)^{3} (- 1) + (x - 1 - 2 i)^{3} \cdot 2 i

= (x - 1 - 2 i)^{3} x + (x - 1 - 2 i)^{3} (- 1) + (x - 1 - 2 i)^{3} \cdot 2 i

Simplify

(x - 1 - 2 i)^{3} x + (x - 1 - 2 i)^{3} (- 1) + (x - 1 - 2 i)^{3} \cdot 2 i : 20 i + x^{4} - 4 x^{3} + 6 x^{2} - 28 x i + 12 x^{2} i - 4 x^{3} i - 4 x - 15

= 20 i + x^{4} - 4 x^{3} + 6 x^{2} - 28 x i + 12 x^{2} i - 4 x^{3} i - 4 x - 15

Rewrite in standard complex form:

(x^{4} - 4 x^{3} + 6 x^{2} - 4 x - 15) + (20 - 28 x + 12 x^{2} - 4 x^{3}) i

= (x^{4} - 4 x^{3} + 6 x^{2} - 4 x - 15) + (20 - 28 x + 12 x^{2} - 4 x^{3}) i

(3 + \frac{3 i}{n})^{2}

(4 + 3) (1 + 3)

\frac{( 4 - r ^{2} ) ^{2}}{2}

\frac{d ^{2}}{d x ^{2}} ((y) y^{2} (6 - 2 x))

\frac{s + e ^{- π s} - e ^{- 2 π s}}{s ( s ^{2} + 1 )}

What is (x-1-2i)^3(x-1+2i) ?
The solution to (x-1-2i)^3(x-1+2i) is (x^4-4x^3+6x^2-4x-15)+(20-28x+12x^2-4x^3)i