Answer
$$sqrt(a+ib)=biqrst+aqrst$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}sqrt(a+ib)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}aqrst+biqrst \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}biqrst+aqrst\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{qrst} $ by $ \left( a+bi\right) $ $$ \color{blue}{qrst} \cdot \left( a+bi\right) = aqrst+biqrst $$ |
| ② | Combine like terms: $$ biqrst+aqrst = biqrst+aqrst $$ |
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