Question

Find the product and fill in the blanks to write in standard complex number form. (5 + 3i)(8 - 2i) = a0 + a1

Answer 1

(5+3i)(8-2i). We will FOIL this out like anything else. 5*8 = 40; 5*2i = 10i; 3i*8 = 24i; 3i*-2i = -6i^2. Putting that all together we have 40+10i+24i-6i^2. Simplifying we have 40+34i-6i^2. i^2 = -1, s0 -6*-1=6. Now let's rewrite. 40+34i+6 = 46 + 34i. That's the product.

Answer 2

Answer: The required standard form of the product is
`46+14i.`

Step-by-step explanation: We are given to find the product of the following two complex numbers and write the answer is standard complex number form.

`(5+3i)(8-2i).`

We know that

a complex number z can be written in standard complex number form as follows :

`z=a+bi.`

Now,

`(5+3i)(8-2i)\\\\=5*8-5*2i+3i*8-3i*2i\\\\=40-10i+24i-6i^2\\\\=40+14i+6~~~~~~~~~~~[\textup{since }i^2=-1]\\\\=46+14i.`

Thus, the required standard form of the product is
`46+14i.`