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

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