A student multiplies (4+5i)(3−2i) incorrectly and obtains 12−10i. What is the student's mistake? Select the two correct answers The student has multiplied the second number by the real part of the first number. The student has only multiplied the real parts and the imaginary parts. The student has multiplied the second number by the imaginary part of the first number. The student has added the real parts and multiplied the imaginary parts. In the multiplication of the imaginary parts, the student forgot to square the i.

B & E

Step-by-step explanation:

Correct way:

(4 + 5i)(3 - 2i)

Do the FOIL method (multiply the First numbers together, the Outer numbers together, the Inner numbers together, and the Last numbers together) to get:

12 - 8i + 15i - 10i^{2}

*Don't forget to square the i*  *i^2 = -1*

12 - 8i + 15i + 10

Combine like terms.

22 + 7i is the correct answer.

If you look back at the correct way to solve the problem and go through each choice, you can see that B) the student has only multiplied the real parts and the imaginary parts, and E) in the multiplication of the imaginary parts, the student forgot to square the i to get 12 - 10i. Sorry if I wasn't able to explain well enough.

im here

step-by-step explanation:

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)