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

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

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

(a + bi)^{3}

35 (22 + 33 + 47)

(z + i)^{2}

2 (7 - 35)