CV17

From Exampleproblems

$\sqrt{7+24i} \,$

Rearranging the coeficient of $i\,$

$\sqrt{7+24i}=\sqrt{7+2(3)(4)(i)}\,$

Adding and subtracting 16 on the right hand side, we get $\sqrt{7+24i}=\sqrt{7+2(3)(4)(i)+16-16} \,$

Simplifying and readjusting $\sqrt{7+24i}=\sqrt{2(3)(4)(i)+4^{2}-9} \,$

again rearranging 9 as a multiple of $i\,$

$\sqrt{7+24i}=\sqrt{2(3i)(4)+4^{2}+(3i)^{2}} \,$

Hence readjusting the values $\sqrt{7+24i}=\sqrt{(3i+4)^{2}} \,$

Hence the value is $\sqrt{7+24i}=3i+4 \,$