simplify 2(x+iy)^2

Solution

simplify

2 (x + i y)^{2}

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

Solution steps

2 (x + i y)^{2}

Expand

(x + i y)^{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

A (- 3, - 4) B (2, 11)

(1 - a cos (x))^{2}

π (482 - \frac{272 2}{15})

2 (x - 2) + cot (x)