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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Complex Numbers

Grade: 10-a Lesson: S2-L8

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Multiply the complex numbers: \$ (2 + 3i) times (4 - i) \$.
2	Step	To multiply two complex numbers, you can use the distributive property and the fact that \$i^2 = −1\$.
3	Step	Let’s perform the multiplication:	\$ (2 + 3i) times (4 - i) \$
4	Hint	Using the distributive property, simplify the expression	\$ 2 times 4 + 2 times (−i) + 3i times 4 + 3i times (−i) \$ \$ 8 − 2i + 12i − 3i^2 \$
5	Step	After defining i as the square root of -1, \$ i^2\$ can be simplified to -1	\$ 8 − 2i + 12i − 3 times (−1) \$ 8 − 2i + 12i + 3 11 + 10i
6	Step	So, \$ (2 + 3i) times (4 - i) = 11 + 10i \$.
7	Choice.A	This option matches the result we obtained: 11 + 10i	11 + 10i
8	Choice.B	This option does not match our result. The real part is 12, but we got 11. The imaginary part is 8i, but we got 10i	12 + 8i
9	Choice.C	This option doesn’t match our result. The real part is 9, but we got 11. The imaginary part is 10i, which matches one part of our result, but the real part is incorrect	9 + 10i
10	Choice.D	This option doesn’t match our result. The real part is 7, but we got 11. The imaginary part is -3i, which is different from our imaginary part 10i	7 - 3i
11	Answer	Option	A
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Multiply the complex numbers: \$ (2 + 3i) times (4 - i) \$.

Step

To multiply two complex numbers, you can use the distributive property and the fact that \$i^2 = −1\$.

Step

Let’s perform the multiplication:

\$ (2 + 3i) times (4 - i) \$

Hint

Using the distributive property, simplify the expression

\$ 2 times 4 + 2 times (−i) + 3i times 4 + 3i times (−i) \$

\$ 8 − 2i + 12i − 3i^2 \$

Step

After defining i as the square root of -1, \$ i^2\$ can be simplified to -1

\$ 8 − 2i + 12i − 3 times (−1) \$
8 − 2i + 12i + 3
11 + 10i

Step

So, \$ (2 + 3i) times (4 - i) = 11 + 10i \$.

Choice.A

This option matches the result we obtained:
11 + 10i

11 + 10i

Choice.B

This option does not match our result. The real part is 12, but we got 11. The imaginary part is 8i, but we got 10i

12 + 8i

Choice.C

This option doesn’t match our result. The real part is 9, but we got 11. The imaginary part is 10i, which matches one part of our result, but the real part is incorrect

9 + 10i

Choice.D

This option doesn’t match our result. The real part is 7, but we got 11. The imaginary part is -3i, which is different from our imaginary part 10i

7 - 3i

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?