Question 1

How to simplify (4-2)(7+3i)

Question 2

$\text{Answer : }\frac{22\text{ - 26i}}{58}$

Given that; ( 4 - 2i) / (7 + 3i)

$\begin{gathered} \frac{(4\text{ - 2i)}}{(7\text{ + 3i)}} \\ \text{Firstly, we n}eed\text{ to find the conjugate of the denominator} \\ \text{The conjugate of (7 + 3i) = (7 - 3i)} \\ \text{Multiply the conjugate by the denominator and numerator} \\ \frac{(4-\text{ 2i)}}{(7\text{ + 3i)}}\text{ x }\frac{(7-3i)}{(7\text{ - 3i)}} \\ \text{Open the parentheses using the distributive property} \\ \frac{4\text{ x 7 - 4 x 3i -2i x 7 -2i(-3i)}}{7\text{ x7 - 7 x 3i + 7 x 3i + 3i x (-3i)}} \\ (28-12i-14i+6i^2)/(49-21i+21i-9i^2) \\ \text{Let i}^2\text{ = -1} \\ \frac{28\text{ - 26i + 6(-1)}}{49\text{ - 9 (-1)}} \\ \frac{28\text{ - 6 - 26i}}{49\text{ + 9}} \\ \frac{22\text{ - 26i}}{58} \end{gathered}$

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