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A day full of math games & activities. Find one near you.
If z₁ = 2 - i, z₂ = 1 + i, find |(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)|
Solution:
z₁ + z₂ + 1 = (2 - i) + (1 + i) + 1 = 4
z₁ - z₂ + 1 = (2 - i) - (1 + i) + 1 = 2 - 2i
(z₁ + z₂ + 1)/ (z₁ - z₂ + 1) = 4 / (2 - 2i)
= 2 / (1 - i)
= 2 (1 + i) / (1 + 1) (Rationalized the denominator)
= 1 + i
Now,
|(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)| = √(12 + 12) = √2.
Hence the value of |(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)| is √2
NCERT Solutions Class 11 Maths Chapter 5 Exercise ME Question 10
If z₁ = 2 - i, z₂ = 1 + i, find |(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)|
Summary:
Hence the value of |(z₁ + z₂ + 1)/ (z₁ - z₂ + 1)| is √2
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