Question

What is the Product of 2+√-121 And 3+√-64? The answer must be as a complex number in standard form. Please help​

Answer 1

`94 + 49i`

Explanation:

Given

`2 + \sqrt{-121` and
`3 + \sqrt{-64`

Required

Determine the products

We have:

`(2 + √(-121)) * (3 + √(-64))`

Factorize:

`2(3 + √(-64)) + √(-121) (3 + √(-64))`

Open Brackets

`6 + 2√(-64)+ 3√(-121) + √(-121) *√(-64)`

`6 + 2√(-64)+ 3√(-121) + √(-121*-64)`

`6 + 2√(-64)+ 3√(-121) + √(7744)`

Expand the expression in square roots

`6 + 2√(-1 * 64)+ 3√(-1 * 121) + √(7744)`

Split roots

`6 + 2√(-1) * √(64)+ 3√(-1) * √(121) + √(7744)`

Take positive square roots of 64, 121 and 7744

`6 + 2√(-1) * 8+ 3√(-1) * 11 + 88`

`6 + 16√(-1)+ 33√(-1)+ 88`

Collect Like Terms

`88 + 6 + 16√(-1)+ 33√(-1)`

`94 + 49√(-1)`

A complex number in standard form is:

`a + bi`

Where

`i = \sqrt{-1`

So:

`94 + 49√(-1)`

=

`94 + 49i`

Hence:

The product of
`2 + \sqrt{-121` and
`3 + \sqrt{-64` is
`94 + 49i`