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

The solution to expand (1+i)^2(x+iy) is -2y+2xi

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

expand

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

- 2 y + 2 x i

Solution steps

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

Expand

(1 + i)^{2} : 2 i

= 2 i (x + i y)

Apply the distributive law:

a (b + c) = ab + a c

2 i (x + i y) = 2 i x + 2 ii y

= 2 i x + 2 ii y

Simplify

2 i x + 2 ii y : 2 x i - 2 y

= 2 x i - 2 y

Rewrite in standard complex form:

- 2 y + 2 x i

= - 2 y + 2 x i

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

(x - \frac{2}{3})^{8}

\frac{8 x - 2}{( x - 1 ) ^{2} ( x + 2 )}

sin^{2} (2 x) \cdot (cot^{2} (x) - tan^{2} (x))