Question

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

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 $i=\sqrt{-1},~~i^2=-1.$

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 $-11+62i.$