Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. 3(7 + i7) + i(7 + i7)
Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. 3(7 + i7) + i(7 + i7)

\[3(7\text{ }+~i7)\text{ }+~i(7\text{ }+~i7)~\]

\[=\text{ }21\text{ }+~i21\text{ }+~i7\text{ }+~{{i}^{2~}}7\]

\[=\text{ }21\text{ }+~i28\text{ }\text{ }7~\]

\[[{{i}^{2}}~=\text{ }-1]\]

\[=\text{ }14\text{ }+~i28\]

Consequently,

\[3\left( 7\text{ }+\text{ }i7 \right)\text{ }+\text{ }i\left( 7\text{ }+\text{ }i7 \right)\text{ }=\text{ }14\text{ }+\text{ }i28\]