Express the following in the form of x+iy : squareroot of 24+10i

Please find below the solution to the asked query:

We have : $\sqrt{24+ 10i}$ , So we express that in form of x  + i y , As :

$$\begin{gathered} \Rightarrow \sqrt{25 - 1 + 10i} \\ \Rightarrow \sqrt{25 + 1 \left(i^2\right) + 10i} ( \mathrm{We} \mathrm{know} i^2 = - 1 ) \\ \Rightarrow \sqrt{5^2 + \left(i^2\right) + 2\left(5\right)\left(i\right)} \\ \Rightarrow \sqrt{{\left( 5 + i\right)}^2} \\ \mathbf{\Rightarrow }\mathbf{5}\mathbf{ }\mathbf{+}\mathbf{ }\mathit{i}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)} \end{gathered}$$
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