Question
Answer
$$(y+4i)^2=8iy+y^2-16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(y+4i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}y^2+8iy+16i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}y^2+8iy+(-16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8iy+y^2-16\end{aligned} $$ | |
| ① | Find $ \left(y+4i\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ y } $ and $ B = \color{red}{ 4i }$. $$ \begin{aligned}\left(y+4i\right)^2 = \color{blue}{y^2} +2 \cdot y \cdot 4i + \color{red}{\left( 4i \right)^2} = y^2+8iy+16i^2\end{aligned} $$ |
| ② | $$ 16i^2 = 16 \cdot (-1) = -16 $$ |
| ③ | Combine like terms: $$ 8iy+y^2-16 = 8iy+y^2-16 $$ |
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