(B) Since the coefficients are real,if $1 + i$ is a root,then its conjugate $1 - i$ must also be a root.The sum of the roots is $(1 + i) + (1 - i) = 2

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(B) Since the coefficients are real,if $1 + i$ is a root,then its conjugate $1 - i$ must also be a root.The sum of the roots is $(1 + i) + (1 - i) = 2$.The product of the roots is $(1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 2$.The quadratic equation is given by $x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0$.Substituting the values,we get $x^2 - 2x + 2 = 0$.

Class 11 Mathematics 4-1.Complex numbers Integral power of iota, Algebraic operations and Equality of complex numbers

Easy

The equation of the smallest degree with real coefficients having $1 + i$ as one of the roots is

A
$x^2 + x + 1 = 0$
B
$x^2 - 2x + 2 = 0$
C
$x^2 + 2x + 2 = 0$
D
$x^2 + 2x - 2 = 0$

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4-1.Complex numbers

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Integral power of iota, Algebraic operations and Equality of complex numbers

Let $z \in \mathbb{C}$ with $\operatorname{Im}(z)=10$ and it satisfies $\frac{2z-n}{2z+n}=2i-1$, where $i=\sqrt{-1}$, for some natural number $n$. Then:

MediumMHT CET 2023

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The real values of $x$ and $y$ for which the equation $(x + iy)(2 - 3i) = 4 + i$ is satisfied,are

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The imaginary part of $\frac{(1 + i)^2}{2 - i}$ is

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The additive inverse of $1 - i$ is

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If $(2x - y + 1) + i(x - 2y - 1) = 2 - 3i$,then the multiplicative inverse of $(x - iy)$ is

MediumTS EAMCET 2022

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The equation of the smallest degree with real coefficients having $1 + i$ as one of the roots is

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