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Ex 4.1, 11 - Chapter 4 Class 11 Complex Numbers
Last updated at Dec. 16, 2024 by Teachoo
Chapter 4 Class 11 Complex Numbers
Concept wise
- Quadaratic equation
- Two complex numbers equal
- Convert to a + ib form
- Identities (square, cube of 2 complex numbers)
-
Division
- Power of i(odd and even)
- Conjugate
- Modulus,argument
- Polar representation
- Proof- Replacing iota with -iota
- Proof- Taking general complex numbers
- Proof- Solving
- Proof- Using modulus conjugate property (Pg 102)
Transcript
Ex5.1, 11 Find the multiplicative inverse of the Complex number 4 – 3𝑖 Multiplicative inverse of z = z – 1 Multiplicative inverse of z = 1/𝑧 Putting z = 4 – 3i multiplicative inverse of 4 – 3i = 1/(4 −3 𝑖) Rationalizing = 1/(4 −3𝑖) ×(4 + 3𝑖)/(4 + 3𝑖) = (4+3i)/(4 −3i)(4 + 3𝑖) Using (a – b ) ( a + b ) = a 2 – b 2 = (4 + 3𝑖)/((4)2−(3𝑖)2) = (4 + 3i)/(16 − 9𝑖2) Putting i 2 = − 1 = (4 + 3𝑖)/(16 −9 (−1) ) = (4 + 3𝑖)/(16 + 9) = (4 + 3𝑖)/25 = 4/25+3/25 𝑖
