Question
Answer
$$sqrt(19.459^2+(55.71i)^2)=sqrt\cdot(-2664)$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}sqrt(19.459^2+(55.71i)^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}sqrt\cdot(361+(55.71i)^2) \xlongequal{ } \\[1 em] & \xlongequal{ }sqrt\cdot(361+(55i)^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}sqrt\cdot(361+3025i^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}sqrt\cdot(361-3025) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}sqrt\cdot(-2664)\end{aligned} $$ | |
| ① | i-i=0i |
| ② | $$ \left( 55i \right)^2 = 55^2i^2 = 3025i^2 $$ |
| ③ | $$ 3025i^2 = 3025 \cdot (-1) = -3025 $$ |
| ④ | Combine like terms: $$ \color{blue}{361} \color{blue}{-3025} = \color{blue}{-2664} $$ |
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