simplify 3(x-iy)^2

Solution

simplify

3 (x - i y)^{2}

(3 x^{2} - 3 y^{2}) - 6 x y i

Solution steps

3 (x - i y)^{2}

Expand

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

= 3 (x^{2} - 2 x y i - y^{2})

Apply the distributive law:

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

3 (x^{2} - 2 x y i - y^{2}) = 3 x^{2} + 3 (- 2 x y i) + 3 (- y^{2})

= 3 x^{2} + 3 (- 2 x y i) + 3 (- y^{2})

3 (- 2 x y i) = - 6 x y i

3 (- y^{2}) = - 3 y^{2}

= 3 x^{2} - 6 x y i - 3 y^{2}

Rewrite in standard complex form:

(3 x^{2} - 3 y^{2}) - 6 x y i

= (3 x^{2} - 3 y^{2}) - 6 x y i

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