What is (x-3)(x-4i)^2 ?

The solution to (x-3)(x-4i)^2 is (x^3-3x^2-16x+48)+(-8x^2+24x)i

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simplify (x-3)(x-4i)^2

simplify

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

(x^{3} - 3 x^{2} - 16 x + 48) + (- 8 x^{2} + 24 x) i

Solution steps

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

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

Expand

(x - 4 i)^{2} : x^{2} - 8 x i - 16

= (x^{2} - 8 x i - 16) (x - 3)

Distribute parentheses

= x^{2} x + x^{2} (- 3) - 8 x i x - 8 x i (- 3) - 16 x - 16 (- 3)

Simplify

x^{2} x + x^{2} (- 3) - 8 x i x - 8 x i (- 3) - 16 x - 16 (- 3) : x^{3} - 3 x^{2} - 8 x^{2} i + 24 x i - 16 x + 48

= x^{3} - 3 x^{2} - 8 x^{2} i + 24 x i - 16 x + 48

Rewrite in standard complex form:

(x^{3} - 3 x^{2} - 16 x + 48) + (- 8 x^{2} + 24 x) i

= (x^{3} - 3 x^{2} - 16 x + 48) + (- 8 x^{2} + 24 x) i

(y + 6)^{2}

(\frac{3}{y} - 1) d y

\frac{9}{s \cdot ( s ^{2} + 9 )}

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

\frac{( x - 3 ) ( x + 2 ) ( x - 1 )}{x ( x - 4 )}

What is (x-3)(x-4i)^2 ?
The solution to (x-3)(x-4i)^2 is (x^3-3x^2-16x+48)+(-8x^2+24x)i