Math Problem Statement

Solve the following complex number problems: 1. (2 + 3i) + (4 - 5i) 2. A number with a real part = 10 and an imaginary part = 3i 3. 3(4 - 5i) 4. (2i - 4) - (3 - 7i)

Solution

Let me extract and solve the problems from the image you've uploaded. Here are the questions I see:


Question 17:
Hasil dari (2+3i)+(45i)(2 + 3i) + (4 - 5i) adalah:
A. 26i2 - 6i
B. 35i3 - 5i
C. 44i4 - 4i
D. 53i5 - 3i
E. 62i6 - 2i

Solution for Question 17:
We add the real and imaginary parts separately:
Real part: 2+4=62 + 4 = 6
Imaginary part: 3i+(5i)=2i3i + (-5i) = -2i
So, the result is 62i6 - 2i.
Answer: E


Question 18:
Bilangan yang bagian riil = 10 dan bagian imajiner = 3i3i adalah:
A. 10+3i10 + 3i
B. 10i+310i + 3
C. 10i3i10i - 3i
D. 103i10 - 3i
E. 10i310i - 3

Solution for Question 18:
The real part is 10, and the imaginary part is 3i3i, so the number is 10+3i10 + 3i.
Answer: A


Question 19:
Hasil dari 3(45i)3(4 - 5i) adalah:
A. 75i7 - 5i
B. 1215i12 - 15i
C. 157i15 - 7i
D. 125i12 - 5i
E. 12i5i12i - 5i

Solution for Question 19:
Distribute the 3 over both terms:
Real part: 3×4=123 \times 4 = 12
Imaginary part: 3×(5i)=15i3 \times (-5i) = -15i
So, the result is 1215i12 - 15i.
Answer: B


Question 20:
Hasil dari (2i4)(37i)(2i - 4) - (3 - 7i) adalah:
A. 7+97 + 9
B. 7+9i-7 + 9i
C. 7i+97i + 9
D. 79i7 - 9i
E. 7i97i - 9

Solution for Question 20:
Distribute the negative sign:
(2i4)(37i)=2i43+7i(2i - 4) - (3 - 7i) = 2i - 4 - 3 + 7i
Combine real and imaginary parts:
Real part: 43=7-4 - 3 = -7
Imaginary part: 2i+7i=9i2i + 7i = 9i
So, the result is 7+9i-7 + 9i.
Answer: B


Would you like further details or explanations on any of the problems? Here are some related questions to expand on this topic:

  1. How do you multiply two complex numbers like (2+3i)(45i)(2 + 3i)(4 - 5i)?
  2. Can you explain how the distributive property applies to complex numbers?
  3. What is the geometric interpretation of adding two complex numbers?
  4. How can you find the conjugate of a complex number, and why is it useful?
  5. How do you calculate the modulus (magnitude) of a complex number like 3+4i3 + 4i?

Tip: When subtracting complex numbers, remember to distribute the negative sign across both the real and imaginary parts!

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Addition of Complex Numbers
Multiplication of Complex Numbers
Distributive Property

Formulas

Addition of complex numbers: (a + bi) + (c + di) = (a + c) + (b + d)i
Multiplication of a complex number by a scalar: k(a + bi) = ka + kbi
Subtraction of complex numbers: (a + bi) - (c + di) = (a - c) + (b - d)i

Theorems

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Suitable Grade Level

Grades 9-11