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MAT2611 Semester 1 Assignment 2 2022

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UNISA MAT2611 Linear Algebra Semester ONE Assignment TWO 2022 solutions. Complex numbers Vector spaces

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MAT2611 SEMESTER 1 ASSIGNMENT 2 2022

Problem 3




𝑀𝑒𝑡ℎ𝑜𝑑 1

1
= 𝑐 + 𝑖𝑑 𝑎 ≠ 0 𝑎𝑛𝑑 𝑏 ≠ 0 ∴ 𝑎 + 𝑖𝑏 ≠ 0
𝑎 + 𝑖𝑏

1
= (𝑐 + 𝑖𝑑)
(𝑎 + 𝑖𝑏)

1
× (𝑎 + 𝑖𝑏) = (𝑐 + 𝑖𝑑) × (𝑎 + 𝑖𝑏)
(𝑎 + 𝑖𝑏)

1 = (𝑐 + 𝑖𝑑)(𝑎 + 𝑖𝑏)

1 = 𝑐(𝑎 + 𝑖𝑏) + 𝑖𝑑(𝑎 + 𝑖𝑏)

1 = 𝑐𝑎 + 𝑖𝑏𝑐 + 𝑖𝑎𝑑 + 𝑖 2 𝑏𝑑

1 = 𝑐𝑎 + 𝑖𝑏𝑐 + 𝑖𝑎𝑑 + (−1)𝑏𝑑

1 = 𝑐𝑎 + 𝑖𝑏𝑐 + 𝑖𝑎𝑑 − 𝑏𝑑

1 = 𝑐𝑎 − 𝑏𝑑 + 𝑖𝑏𝑐 + 𝑖𝑎𝑑

1 + 0𝑖 = (𝑐𝑎 − 𝑏𝑑) + 𝑖(𝑏𝑐 + 𝑎𝑑)

𝑐𝑎 − 𝑏𝑑 = 1 (1)
𝑏𝑐 + 𝑎𝑑 = 0 (2)

𝐹𝑟𝑜𝑚 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 (2),
𝑏𝑐 = −𝑎𝑑
𝑎𝑑
𝑐=− (𝑟𝑒𝑐𝑎𝑙𝑙 𝑡ℎ𝑎𝑡 𝑏 ≠ 0)
𝑏

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  • mat2611
  • complex numbers
  • vector spaces
  • linear algebra

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