Lesson Example Discussion Quiz: Class Homework |
Step-5 |
Title: Multiplication of complex numbers |
Grade: 8-b Lesson: S2-L6 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Determine the result when multiplying the complex numbers \$3(6 - 10i)\$ and \$2(10 + 13i)\$. |
|
2 |
Step |
The given expression |
\$3(6 - 10i)\$ times \$2(10 + 13i)\$ |
3 |
Step |
Simplify each complex number seprately \$3(6 - 10i)\$: |
\$3(6 - 10i) = 3 times 6 - 3 times 10i\$ 18 - 30i |
4 |
Step |
Simplify each complex number seprately \$2(10 + 13i)\$: |
\$2(10 + 13i) = 2 times 10 + 2 times 13i\$ 20 + 26i |
5 |
Step |
Now, multiply the simplified complex numbers: |
\$(18 - 30i) times (20 + 26i)\$ |
6 |
Hint |
Expand this using the distributive property (FOIL method): |
\$ 18 times 20 + 18 times 26i times - 30i times 20 - 30i times 26i\$ |
7 |
Step |
Calculate each term: |
\$ 360 + 468i - 600i - 780i^2\$ |
8 |
Hint |
Since \$i^2 = - 1\$. |
|
9 |
Step |
Plug the \$i^2 = - 1\$ in the above expression and then simplify it: |
\$360 + 468i -600i - 780(-1)\$ 360 - 132i + 780 1140 - 132i |
10 |
Step |
So, the multiplying complex number is 1140 - 132i. |
|
11 |
Choice.A |
Correct: Because it has accurately done the multiplication of given complex numbers |
1140 - 132i |
12 |
Choice.B |
Option B is incorrect because it yields 1401−132i, whereas our result is 1140−132i |
1401- 132i |
13 |
Choice.C |
The imaginary part should be - 132i, not +132i. So, this is wrong choice |
1140 + 132i |
14 |
Choice.D |
1401 + 132i is not correct because the real part and imaginary part do not match the result of the multiplication |
1401 +132i |
15 |
Answer |
Option |
A |
16 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
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