If point A(2 + i) is rotated about origin with angle pi/4 in anticlockwise direction to reach at B, then B is
Answers
Given : A(2 + i) is rotated about origin with angle pi/4 in anticlockwise direction to reach at B
To Find : B
Solution:
A = 2 + i
| A |² = 2² + 1² = 5
Angle = Tan⁻¹( 1/2)
New Angle = Tan⁻¹( 1/2) + π/4
Tan (Tan⁻¹( 1/2) + π/4)
using Tan(A + B) = (Tan A + Tan B ) /(1 - TanATanB)
Tan (Tan⁻¹( 1/2)) = 1/2 and Tan π/4 = 1
= (1/2 + 1)/(1 - (1/2)1)
= (3/2)/(1/2)
= 3
New Position = x + iy
y/x = 3
=> y = 3x
x² + y² = 5
=> x² + (3x)² = 5
=> x² + 9x² = 5
=> 10x² = 5
=> x² = 1/2
=> x = 1/√2
y = 3/√2
1/√2 + i 3/√2
= (1 + 3i)/√2
B is (1 + 3i)/√2
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Answer:Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The earliest roots of science can be traced to Ancient Egypt and Mesopotamia in around 3500 to 3000 BCE. Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The earliest roots of science can be traced to Ancient Egypt and Mesopotamia in around 3500 to 3000 BCE.
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