Respuesta :
The product of (3 + 2i) and a complex number is (17 + 7i)
The product of (3 + 2i) and a complex number is (17 + 7i).
Let the complex number be a + ib
Product means we multiply
So (3+2i) * (a + ib) = (17+7i)
WE need to find a+ ib
Divie by 3 + 2i on both sides
a + ib = (17+7i) / (3+2i)
To divide multiply by the conjugate (3-2i)
[tex]a + ib = (\frac{ 17+7i)*(3-2i)}{(3+2i)(3-2i)}[/tex]
[tex]a + ib = (\frac{(17*3+7*2)+(7*3-17*2)i}{3^2-2^2}[/tex]
[tex]a + ib = (\frac{(65)+(-13)i}{13}[/tex]
[tex]a+ib = \frac{65}{13} - \frac{13}{13}[/tex]
a+ib = 5 - i
The required complex number is 5 - i
Answer:
37+55i
Step-by-step explanation:
The product of (3 + 2i) and a complex number is (17 + 7i) is expressed as shown below:
(3+2i)(17+7i)
Expanding the bracket,
= 51+21i+34i+14i²
= 51+55i+14i²
Note that in complex numbers i² = -1
Substituting this into the result, we have:
= 51+55i+14(-1)
= 51+55i-14
= 37+55i
The product of both complex number is 37+55i