EQUALITY, ADDITION AND SUBTRACTION OF COMPLEX NUMBERS

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Equality of a complex number

Two complex numbers are said to be equal, if their real and imaginary parts are equal.

Example:

a + bi = c + di, then, a = c,b = d

Addition and subtraction of a complex number

Addition or subtraction of real part and imaginary part is done separately.

Addition or subtraction of complex number is defined as follows:

Addition

\left( {a + bi} \right) + \left( {c + di} \right) = \left( {a + c} \right) + \left( {b + d} \right)i

Subtraction

\left( {a + bi} \right) - \left( {c + di} \right) = \left( {a - c} \right) + \left( {b - d} \right)i

Example

Solve\left( {3 + 5i} \right) - \left( {2 - 7i} \right)

\begin{array}{c}
\left( {3 + 5i} \right) - \left( {2 - 7i} \right) = 3 + 5i - 2 + 7i\\
 = 3 - 2 + 5i + 7i\\
 = 1 + 12i
\end{array}

Question 1

Solve\left( {7 + 10i} \right) - \left( {6 - 12i} \right)

Solution

\begin{array}{c}
\left( {7 + 10i} \right) - \left( {6 - 12i} \right) = 7 + 10i - 6 + 12i\\
 = 7 - 6 + 10i + 12i\\
 = 1 + 22i
\end{array}

Question 2

Solve2\left( {5 + 7i} \right) - 2\left( {3 - 4i} \right)

Solution

\begin{array}{c}
2\left( {5 + 7i} \right) - 2\left( {3 - 4i} \right) = 10 + 14i - 6 + 8i\\
 = 10 - 6 + 14i + 8i\\
 = 4 + 22i
\end{array}

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