Question

find the following product and write the result in standard form, ( a + bi ).( (-2 + 6i)(5 + i) )( (-2 + 6i)(5 + i)=square )

Explanation:

Step1: Apply distributive property (FOIL)

$(-2)(5) + (-2)(i) + (6i)(5) + (6i)(i)$

Step2: Calculate each term

$-10 - 2i + 30i + 6i^2$

Step3: Substitute $i^2=-1$

$-10 - 2i + 30i + 6(-1)$

Step4: Simplify real terms

$-10 -6 -2i + 30i$

Step5: Combine like terms

$-16 + 28i$

Answer:

$-16 + 28i$