Complex Numbers
Mediummathematics
If z₁ = 2 + 3i and z₂ = 1 - 2i, then z₁ × z₂ equals
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Solution
Incorrect! Answer:
8 - i
- Distributive Property: Multiply the two complex numbers like binomials:
- z1×z2=(2+3i)(1−2i)
- Expansion:
- =2(1)+2(−2i)+3i(1)+3i(−2i)
- =2−4i+3i−6i2
- Substitute i2=−1:
- =2−i−6(−1)
- =2−i+6
- Combine Real and Imaginary:
- =8−i.
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About This Question
- Subject
- mathematics
- Chapter
- complex numbers and quadratic equations
- Topic
- complex numbers
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
8 - i
- Distributive Property: Multiply the two complex numbers like binomials:
- z1×z2=(2+3i)(1−2i)
- Expansion:
- =2(1)+2(−2i)+3i(1)+3i(−2i)
- =2−4i+3i−6i2
- Substitute i2=−1:
- =2−i−6(−1)
- =2−i+6
- Combine Real and Imaginary:
- =8−i.
This medium difficulty mathematics question is from the chapter complex numbers and quadratic equations, covering the topic of complex numbers. It appeared in the 2025 exam.
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