Question
Answer
$$i\cdot(1-sqrt\cdot3i)(sqrt\cdot3+i)=-9i^2q^2r^2s^2t^2-3i^3qrst+3iqrst+i^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}i\cdot(1-sqrt\cdot3i)(sqrt\cdot3+i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1i-3i^2qrst)(sqrt\cdot3+i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3iqrst+i^2-9i^2q^2r^2s^2t^2-3i^3qrst \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-9i^2q^2r^2s^2t^2-3i^3qrst+3iqrst+i^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{i} $ by $ \left( 1-3iqrst\right) $ $$ \color{blue}{i} \cdot \left( 1-3iqrst\right) = i-3i^2qrst $$ |
| ② | Multiply each term of $ \left( \color{blue}{i-3i^2qrst}\right) $ by each term in $ \left( 3qrst+i\right) $. $$ \left( \color{blue}{i-3i^2qrst}\right) \cdot \left( 3qrst+i\right) = 3iqrst+i^2-9i^2q^2r^2s^2t^2-3i^3qrst $$ |
| ③ | Combine like terms: $$ -9i^2q^2r^2s^2t^2-3i^3qrst+3iqrst+i^2 = -9i^2q^2r^2s^2t^2-3i^3qrst+3iqrst+i^2 $$ |
This page was created using
Complex Expression calculator