simplify (2xy+iy)^2

Solution

simplify

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

(4 x^{2} y^{2} - y^{2}) + 4 x y^{2} i

Solution steps

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

Apply Perfect Square Formula:

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

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

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

(2 x y)^{2} = 4 x^{2} y^{2}

2 \cdot 2 x y i y = 4 x i y^{2}

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

= 4 x^{2} y^{2} + 4 x i y^{2} - y^{2}

Rewrite in standard complex form:

(4 x^{2} y^{2} - y^{2}) + 4 x y^{2} i

= (4 x^{2} y^{2} - y^{2}) + 4 x y^{2} i

2 + \frac{2 ( 8 + π )}{16}

\frac{3}{2 ( 3 a - 5 )}

(2 x + \frac{3}{y}) (2 x - \frac{3}{y})

x^{2} (2 cos (x) - 4 x sin (x) - x^{2} cos (x))