What is (x^2+4)^2(x+2i)^2 ?

The solution to (x^2+4)^2(x+2i)^2 is (x^6+4x^4-16x^2-64)+(4x^5+32x^3+64x)i

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simplify (x^2+4)^2(x+2i)^2

simplify

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

(x^{6} + 4 x^{4} - 16 x^{2} - 64) + (4 x^{5} + 32 x^{3} + 64 x) i

Solution steps

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

Expand

(x^{2} + 4)^{2} : x^{4} + 8 x^{2} + 16

= (x^{4} + 8 x^{2} + 16) (x + 2 i)^{2}

= (x + 2 i)^{2} (x^{4} + 8 x^{2} + 16)

Expand

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

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

Distribute parentheses

= x^{2} x^{4} + x^{2} \cdot 8 x^{2} + x^{2} \cdot 16 + 4 x i x^{4} + 4 x i 8 x^{2} + 4 x i 16 - 4 x^{4} - 4 \cdot 8 x^{2} - 4 \cdot 16

Simplify

x^{2} x^{4} + x^{2} \cdot 8 x^{2} + x^{2} \cdot 16 + 4 x i x^{4} + 4 x i 8 x^{2} + 4 x i 16 - 4 x^{4} - 4 \cdot 8 x^{2} - 4 \cdot 16 : x^{6} + 4 x^{4} - 16 x^{2} + 4 x^{5} i + 32 x^{3} i + 64 x i - 64

= x^{6} + 4 x^{4} - 16 x^{2} + 4 x^{5} i + 32 x^{3} i + 64 x i - 64

Rewrite in standard complex form:

(x^{6} + 4 x^{4} - 16 x^{2} - 64) + (4 x^{5} + 32 x^{3} + 64 x) i

= (x^{6} + 4 x^{4} - 16 x^{2} - 64) + (4 x^{5} + 32 x^{3} + 64 x) i

A (- 1, 5) B (5, - 4)

(- 4 x + 5) (\frac{3}{2})

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

\frac{- x ^{2} + 2 x + 4}{( x ^{2} + 4 ) ^{2}}

R A TE (5, 94.25, - 270.34 - 40)

What is (x^2+4)^2(x+2i)^2 ?
The solution to (x^2+4)^2(x+2i)^2 is (x^6+4x^4-16x^2-64)+(4x^5+32x^3+64x)i