Question:
Let \(\bar{z}\) denote the complex conjugate of a complex number \(z\) and let \(i=\sqrt{-1}\) In the set of complex numbers, the number of distinct roots of the equation \(\bar{z}-z^2=i\left(\bar{z}+z^2\right)\) is ___
Let \(\bar{z}\) denote the complex conjugate of a complex number \(z\) and let \(i=\sqrt{-1}\) In the set of complex numbers, the number of distinct roots of the equation \(\bar{z}-z^2=i\left(\bar{z}+z^2\right)\) is ___
Updated On: Apr 23, 2024
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Correct Answer: 4
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The correct answer is 4
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Concepts Used:
Complex Number
A Complex Number is written in the form
a + ib
where,
- “a” is a real number
- “b” is an imaginary number
The Complex Number consists of a symbol “i” which satisfies the condition i^2 = −1. Complex Numbers are mentioned as the extension of one-dimensional number lines. In a complex plane, a Complex Number indicated as a + bi is usually represented in the form of the point (a, b). We have to pay attention that a Complex Number with absolutely no real part, such as – i, -5i, etc, is called purely imaginary. Also, a Complex Number with perfectly no imaginary part is known as a real number.