Question
Answer
$$(1+9i)(i+9i)=10i-90$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(1+9i)(i+9i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1+9i)\cdot10i \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10i+90i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10i-90\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{i} + \color{blue}{9i} = \color{blue}{10i} $$ |
| ② | $$ \left( \color{blue}{1+9i}\right) \cdot 10i = 10i+90i^2 $$ |
| ③ | $$ 90i^2 = 90 \cdot (-1) = -90 $$ |
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