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

Respuesta :

Luv2Teach
(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:  The required standard form of the product is [tex]46+14i.[/tex]

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.

[tex](5+3i)(8-2i).[/tex]

We know that

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

[tex]z=a+bi.[/tex]

Now,

[tex](5+3i)(8-2i)\\\\=5\times8-5\times2i+3i\times8-3i\times2i\\\\=40-10i+24i-6i^2\\\\=40+14i+6~~~~~~~~~~~[\textup{since }i^2=-1]\\\\=46+14i.[/tex]

Thus, the required standard form of the product is [tex]46+14i.[/tex]

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