Question

1. write the expression in standard form: \\(\frac{2}{3 - 13i}\\)

Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by $3+13i$:
$$\frac{2}{3-13i} \times \frac{3+13i}{3+13i} = \frac{2(3+13i)}{(3)^2 - (13i)^2}$$

Step2: Expand denominator

Calculate denominator using $i^2=-1$:
$$(3)^2 - (13i)^2 = 9 - (-169) = 178$$

Step3: Simplify expression

Distribute 2 in numerator and split fraction:
$$\frac{6 +26i}{178} = \frac{6}{178} + \frac{26}{178}i = \frac{3}{89} + \frac{13}{89}i$$

Answer:

$\frac{3}{89} + \frac{13}{89}i$