CV17

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

Rearranging the coeficient ofi\,

{\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 ofi\,

{\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\,

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