Tap the blue circles to see an explanation.
$$ \begin{aligned}i^{243}\cdot(1-3i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-i\cdot(1-3i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-i+3i^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-i-3\end{aligned} $$ | |
① | $$ i^{243} = i^{4 \cdot 60 + 3} =
\left( i^4 \right)^{ 60 } \cdot i^3 =
1^{ 60 } \cdot (-i) =
-i = -i $$ |
② | Multiply $ \color{blue}{-i} $ by $ \left( 1-3i\right) $ $$ \color{blue}{-i} \cdot \left( 1-3i\right) = -i+3i^2 $$ |
③ | $$ 3i^2 = 3 \cdot (-1) = -3 $$ |