simplify (y+4i)^2

Solution

simplify

(y + 4 i)^{2}

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

Solution steps

(y + 4 i)^{2}

Apply Perfect Square Formula:

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

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

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

2 y \cdot 4 i = 8 y i

(4 i)^{2} = - 16

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

Rewrite in standard complex form:

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

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

3 \times 1 0^{- 3}

\frac{9}{8} m + \frac{9}{10} - 2 m - \frac{3}{5}

lo g_{0.5} (\frac{1}{2})

\frac{95}{3} 5

5 i - 54