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.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

5

10

15

20

25

30

35

40

45

50

55