Answer
$$(4z+5i)^2=40iz+16z^2-25$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4z+5i)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}16z^2+40iz+25i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}16z^2+40iz+(-25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}40iz+16z^2-25\end{aligned} $$ | |
| ① | Find $ \left(4z+5i\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 4z } $ and $ B = \color{red}{ 5i }$. $$ \begin{aligned}\left(4z+5i\right)^2 = \color{blue}{\left( 4z \right)^2} +2 \cdot 4z \cdot 5i + \color{red}{\left( 5i \right)^2} = 16z^2+40iz+25i^2\end{aligned} $$ |
| ② | $$ 25i^2 = 25 \cdot (-1) = -25 $$ |
| ③ | Combine like terms: $$ 40iz+16z^2-25 = 40iz+16z^2-25 $$ |
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