Answer:
[tex]94 + 49i[/tex]
Step-by-step explanation:
Given
[tex]2 + \sqrt{-121[/tex] and [tex]3 + \sqrt{-64[/tex]
Required
Determine the products
We have:
[tex](2 + \sqrt{-121}) * (3 + \sqrt{-64})[/tex]
Factorize:
[tex]2(3 + \sqrt{-64}) + \sqrt{-121} (3 + \sqrt{-64})[/tex]
Open Brackets
[tex]6 + 2\sqrt{-64}+ 3\sqrt{-121} + \sqrt{-121} *\sqrt{-64}[/tex]
[tex]6 + 2\sqrt{-64}+ 3\sqrt{-121} + \sqrt{-121*-64}[/tex]
[tex]6 + 2\sqrt{-64}+ 3\sqrt{-121} + \sqrt{7744}[/tex]
Expand the expression in square roots
[tex]6 + 2\sqrt{-1 * 64}+ 3\sqrt{-1 * 121} + \sqrt{7744}[/tex]
Split roots
[tex]6 + 2\sqrt{-1} * \sqrt{64}+ 3\sqrt{-1} * \sqrt{121} + \sqrt{7744}[/tex]
Take positive square roots of 64, 121 and 7744
[tex]6 + 2\sqrt{-1} * 8+ 3\sqrt{-1} * 11 + 88[/tex]
[tex]6 + 16\sqrt{-1}+ 33\sqrt{-1}+ 88[/tex]
Collect Like Terms
[tex]88 + 6 + 16\sqrt{-1}+ 33\sqrt{-1}[/tex]
[tex]94 + 49\sqrt{-1}[/tex]
A complex number in standard form is:
[tex]a + bi[/tex]
Where
[tex]i = \sqrt{-1[/tex]
So:
[tex]94 + 49\sqrt{-1}[/tex]
=
[tex]94 + 49i[/tex]
Hence:
The product of [tex]2 + \sqrt{-121[/tex] and [tex]3 + \sqrt{-64[/tex] is [tex]94 + 49i[/tex]
