simplify i(x-iy)^2

Solution

simplify

i (x - i y)^{2}

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

Solution steps

i (x - i y)^{2}

Expand

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

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

Apply the distributive law:

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

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

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

i x^{2} = x^{2} i

i (- 2 x y i) = 2 x y

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

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

Rewrite in standard complex form:

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

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

\frac{8}{( x - 1 ) ( x + 1 ) ( x + 3 )}

\frac{18 s ^{2}}{( s + 1 ) ( s + 4 )}

A (- 2, - 3) y B (2, 2)

6 (1 + \frac{1}{3 s})

a + b - 2 c - 3 a + 3 b + 2 (a + b + c)