Example 6  - Express in a + ib (i) (5 + root 2 i) - Examples

  1. Chapter 5 Class 11 Complex Numbers
  2. Serial order wise
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Example 6 Express the following in the form a + ib (5 + √2 i )/(1 βˆ’ √2 i) (5 + √2 𝑖 )/(1 βˆ’ √2 𝑖) Rationalizing = (( 5 + √2 𝑖) )/((1 βˆ’ √2 𝑖 ) ) Γ— ((1 + √2 𝑖))/((1 + √2 𝑖) ) = (( 5 + √2 𝑖) (1 + √2 𝑖 ))/((1 βˆ’ √2 𝑖 ) (1 + √2 𝑖) ) = ( ( 5 + √2 𝑖 ) ( 1 +√2 𝑖))/(( 1 )2 βˆ’ (√2 𝑖 )2) = ( ( 5 + √2 𝑖 ) ( 1 +√2 𝑖) )/(1 βˆ’ 2𝑖 2) = ( 5 Γ— 1 + 5 Γ— √2 𝑖 + √2 𝑖 Γ— 1 + √2 𝑖 Γ— √2 𝑖)/(1 βˆ’2𝑖2) = ( 5 + 5 √2 𝑖 + √2 𝑖 + 2𝑖2)/(1 βˆ’2𝑖2) Putting i 2 = βˆ’1 = ( 5 + 5√2 𝑖 + √2 𝑖 + 2 ( βˆ’ 1 ))/(1 βˆ’2 ( βˆ’1 )) = ( 5 + 5 √2 𝑖 + √2 𝑖 βˆ’ 2)/(1 + 2) = ( 5 βˆ’2 +5 √2 𝑖 +√2 𝑖)/3 = ( 3 + 6 √2 𝑖 )/3 = ( 3 ( 1+2 √2 𝑖 ))/3 = 1 + 2 √2 𝑖 Example 6 Express the following in the form a+ ib (ii) 𝑖^(βˆ’35) 𝑖^(βˆ’35) = 1/𝑖^35 = 1/(γ€–(𝑖〗^34) Γ— 𝑖) = 1/((𝑖^2 )^17 Γ— 𝑖 ) Putting i 2 = βˆ’ 1 = 1/(( βˆ’1 ) 17 Γ— 𝑖) = 1/("βˆ’" 1Γ— 𝑖) = 1/(βˆ’ 𝑖) Multiplying and divided by – 𝑖 = 1/(βˆ’ 𝑖) Γ— (βˆ’ 𝑖)/(βˆ’ 𝑖) = (βˆ’ 𝑖 )/( 𝑖^2 ) Putting i 2 = βˆ’ 1 = (βˆ’ 𝑖 )/( 𝑖 ) = 𝑖 = 0 + 𝑖

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