simplify (1+4yi)^2

Solution

simplify

(1 + 4 y i)^{2}

(1 - 16 y^{2}) + 8 y i

Solution steps

(1 + 4 y i)^{2}

Apply Perfect Square Formula:

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

(1 + 4 y i)^{2} = 1^{2} + 2 \cdot 1 \cdot 4 y i + (4 y i)^{2}

= 1^{2} + 2 \cdot 1 \cdot 4 y i + (4 y i)^{2}

1^{2} = 1

2 \cdot 1 \cdot 4 y i = 8 y i

(4 y i)^{2} = - 16 y^{2}

= 1 + 8 y i - 16 y^{2}

Rewrite in standard complex form:

(1 - 16 y^{2}) + 8 y i

= (1 - 16 y^{2}) + 8 y i

(cot (x) - 3) (csc (x) + 2)

(3 x y^{2} - 4 y) + (3 x - 4 x^{2} y) \frac{d y}{d x}

(x^{2} + 6) (1 - x)

(1 + \frac{2 i}{n})^{2}

(- 1 + i 3)^{11}