Question

What is the product of 6+5i and 4+7i?

Enter your answer, in standard form, in the box.
______

Answer 1

The answer to this question is the product is 12i

Answer 2

Answer: The required product is
`-11+62i.`

Step-by-step explanation: We are given to find the product of the following two complex numbers :

`z_1=6+5i,~~~z_2=4+7i.`

We will be using the following property :

`(a+b)(c+d)=a(c+d)+b(c+d).`

Also, we will use the fact that
`i=√(-1),~~i^2=-1.`

The product of the given complex numbers is

`z_1z_2\\\\=(6+5i)(4+7i)\\\\=6(4+7i)+5i(4+7i)\\\\=24+42i+20i+35i^2\\\\=24+62i-35\\\\=-11+62i.`

Thus, the required product is
`-11+62i.`