eCompNoOperation

Example Answer the following questions:

$\displaystyle z_{1} = 3+2i, z_{2} = 4+ 5i$

$\begin{displaymath}\begin{array}{ll} 1. & z_{1} + z_{2}\\ 2. & z_{1}z_{2}\\ 3. & z_{2}/z_{1} \end{array}\end{displaymath}$

Answer A sum of $z_{1}$ and $z_{2}$ is the sum of real parts and the sum of imaginary parts.

$\displaystyle z_{1} + z_{2} = 3+2i + 4+5i = 3+4 + (2+5)i = 7 + 7i$

A real part of a product of the $z_1$

and

is difference of the product of real parts and the product of imaginary parts. Then

$\displaystyle z_{1}z_{2} = (3+2i)(4+5i) = 12-10+(15+8)i = 2+23i$

A quotient of two complex numbers can be rationalized by multiplying the conjugate of the denominator，

$\displaystyle z_{2}/z_{1} = \frac{4+5i}{3+2i} = \frac{(4+5i)(3-2i)}{(3+2i)(3-2i)} = \frac{22+7i}{13}$