Respuesta :
Answer:
1. In the multiplication of the imaginary parts, the student forgot to square of i. OR
2. The student has only multiplied the real parts and the imaginary parts.
Correct value [tex]=22+7i[/tex].
Step-by-step explanation:
The given expression is
[tex](4+5i)(3-2i)[/tex]
A student multiplies (4+5i) (3-2i) incorrectly and obtains 12-10i.
Student's mistake can be either 1 or second:
1. In the multiplication of the imaginary parts, the student forgot to square of i.
2. The student has only multiplied the real parts and the imaginary parts.
[tex](4+5i)(3-2i)=4\times 3+5\times (-2)i=12-10i[/tex]
Which is not correct. The correct steps are shown below.
Using distributive property, we get
[tex]4(3-2i)+5i(3-2i)[/tex]
[tex]4(3)+4(-2i)+5i(3)+5i(-2i)[/tex]
[tex]12-8i+15i-10i^2[/tex]
[tex]12+7i-10(-1)[/tex] [tex][\because i^2=-1][/tex]
[tex]12+7i+10[/tex]
[tex]22+7i[/tex]
Therefore, the correct value of [tex](4+5i)(3-2i)[/tex] is [tex]22+7i[/tex].
