simplify (3x-yi)^2

Solution

simplify

(3 x - y i)^{2}

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

Solution steps

(3 x - y i)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

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

(3 x)^{2} = 9 x^{2}

- 2 \cdot 3 x y i = - 6 x y i

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

= 9 x^{2} - 6 x y i - y^{2}

Rewrite in standard complex form:

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

= (9 x^{2} - y^{2}) - 6 x y i

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