Answer
$$(5(cos\cdot20+isin\cdot20))^3=1000000i^6n^3s^3+3000000ci^4n^2os^3+3000000c^2i^2no^2s^3+1000000c^3o^3s^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5(cos\cdot20+isin\cdot20))^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(5(20cos+20i^2ns))^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(100cos+100i^2ns)^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}1000000c^3o^3s^3+3000000c^2i^2no^2s^3+3000000ci^4n^2os^3+1000000i^6n^3s^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}1000000i^6n^3s^3+3000000ci^4n^2os^3+3000000c^2i^2no^2s^3+1000000c^3o^3s^3\end{aligned} $$ | |
| ① | $$ i s i n \cdot 20 = 20 i^{1 + 1} n s = 20 i^2 n s $$ |
| ② | Multiply $ \color{blue}{5} $ by $ \left( 20cos+20i^2ns\right) $ $$ \color{blue}{5} \cdot \left( 20cos+20i^2ns\right) = 100cos+100i^2ns $$ |
| ③ | Find $ \left(100cos+100i^2ns\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = 100cos $ and $ B = 100i^2ns $. $$ \left(100cos+100i^2ns\right)^3 = \left( 100cos \right)^3+3 \cdot \left( 100cos \right)^2 \cdot 100i^2ns + 3 \cdot 100cos \cdot \left( 100i^2ns \right)^2+\left( 100i^2ns \right)^3 = 1000000c^3o^3s^3+3000000c^2i^2no^2s^3+3000000ci^4n^2os^3+1000000i^6n^3s^3 $$ |
| ④ | Combine like terms: $$ 1000000i^6n^3s^3+3000000ci^4n^2os^3+3000000c^2i^2no^2s^3+1000000c^3o^3s^3 = \\ = 1000000i^6n^3s^3+3000000ci^4n^2os^3+3000000c^2i^2no^2s^3+1000000c^3o^3s^3 $$ |
This page was created using
Complex Expression calculator