simplify 2(x+yi)^2

Solution

simplify

2 (x + y i)^{2}

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

Solution steps

2 (x + y i)^{2}

Expand

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

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

Apply the distributive law:

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

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

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

2 \cdot 2 x y i = 4 x y i

2 (- y^{2}) = - 2 y^{2}

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

Rewrite in standard complex form:

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

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

\frac{z + 16}{z ^{2} ( z - 1 )}

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\frac{1}{( 1 + x ) ^{6}}

- 7 x^{2} l e f t (x y + 3 x^{5} y)