Real and Imaginary parts MCQ Quiz in मराठी - Objective Question with Answer for Real and Imaginary parts - मोफत PDF डाउनलोड करा
Last updated on Mar 13, 2025
Latest Real and Imaginary parts MCQ Objective Questions
Real and Imaginary parts Question 1:
समजा \(z \in \mathbb{C}\) हा संमिश्र संख्यांचा संच आहे. तर समीकरण, \(2|z+3i|-|z-i|=0\) दर्शवते.
Answer (Detailed Solution Below)
Real and Imaginary parts Question 1 Detailed Solution
\(2|z+3i|-|z-i|=0\)
\(2|x+i(y+3)|=|x+i(y-1)|\) .......... \(z=x+iy\)
\(2 \sqrt{x^2+(y+3)^2} = \sqrt{x^2+(y-1)^2}\)
\(4x^2+4(y+3)^2=x^2+(y-1)^2\)
\(3x^2 = y^2 - 2y + 1 - 4y^2 - 24y - 36\)
\(3x^2 + 3y^2 + 26y + 35 = 0\)
\(x^2 + y^2 + \frac{26}{3} y + \frac{35}{3} = 0\)
हे वर्तुळाचे समीकरण आहे.
म्हणून, त्रिज्या \( = r = \sqrt{0 + \frac{169}{9} - \frac{35}{3}}\)
\(= \sqrt{\frac{64}{9}}\)
\(= \frac{8}{3}\)
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Real and Imaginary parts Question 2:
समजा \(z \in \mathbb{C}\) हा संमिश्र संख्यांचा संच आहे. तर समीकरण, \(2|z+3i|-|z-i|=0\) दर्शवते.
Answer (Detailed Solution Below)
Real and Imaginary parts Question 2 Detailed Solution
\(2|z+3i|-|z-i|=0\)
\(2|x+i(y+3)|=|x+i(y-1)|\) .......... \(z=x+iy\)
\(2 \sqrt{x^2+(y+3)^2} = \sqrt{x^2+(y-1)^2}\)
\(4x^2+4(y+3)^2=x^2+(y-1)^2\)
\(3x^2 = y^2 - 2y + 1 - 4y^2 - 24y - 36\)
\(3x^2 + 3y^2 + 26y + 35 = 0\)
\(x^2 + y^2 + \frac{26}{3} y + \frac{35}{3} = 0\)
हे वर्तुळाचे समीकरण आहे.
म्हणून, त्रिज्या \( = r = \sqrt{0 + \frac{169}{9} - \frac{35}{3}}\)
\(= \sqrt{\frac{64}{9}}\)
\(= \frac{8}{3}\)