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- Question 9, Exercise 1.2
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... x_2 = 2, \quad y_2 = 5.\] First, we need to compute \(x_1^2 + y_1^2\): \[x_1^2 + y_1^2 = 4^2 + 2^2 = 20.\] Next, compute \(x_2^2 - y_2^2\): \[x_2^2 - y_2^2 = 2^2 - 5^2 = -21.\] Then, compute \(x_1^2 - y_1^2\): \[x_1^2 - y_1^2 = 4^2 - 2^
- Question 8, Exercise 1.2
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... $z=x+i y$. **Solution.** Given: $$|2z-i|=4.$$ Put $z=x+i y$, we have \begin{align} & |2(x+iy)-i|=4... y$. **Solution.** Given: $$|z-1|=|\bar{z}+i|.$$ Put $z=x+iy$, we have \begin{align} & |(x+iy)-1| = |... **Solution.** Given: $$|z-4i| + |z+4i| = 10.$$ Put $z = x + iy$, we have \begin{align} & |(x + iy)
- Question 4, Exercise 1.1
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... {align} &3x=-3y \\ x=-y \quad ... (3) \end{align} Putting value of $x$ in (1) \begin{align}2(-y)+y+2&=0\\ -2y+y&=-2\\ -y&=-2\\ y&=2\end{align} Putting in $(3)$, we have $x=-2$. Hence $x=-2$ and ... (2)$, we have &y=2x-1\cdots \cdots (3)\end{align} Put the value of $y$ in $(1)$ \begin{align}& x+(2x-1
- Question 3, Exercise 1.2
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... hat for $z \in \mathbb{C}$. $z$ is either real or pure imaginary iff $(\overline{z})^{2}=z^{2}$. **So... For $z=x+iy$, first suppose that $z$ is real or pure imaginary, then $$z=x \quad \text{ or } \quad z... ither $z=iy$ or $z=x$. This gives $z$ is real or pure imaginary. ====Go to ==== <text align="left"><b
- Question 4, Exercise 1.3
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... {106}\\ &=\dfrac{2}{53}-\dfrac{7}{53}i\end{align} Put value of $\omega$ in (1), we have \begin{align} ... a= -\dfrac{288}{109}+ \dfrac{88}{109}i\end{align} Put vale of $\omega$ in $(1)$, we have \begin{align}... 53}\\ &=\dfrac{68}{53}-\dfrac{80}{53}i\end{align} Putting value of $\omega$ in $(3)$, we get \begin{al
- Question 1, Exercise 1.3
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... **Solution.** Given: $$z^{3}+2 z^{2}-23 z-60$$ Putting $z = -3$: \begin{align} (-3)^3 + 2(-3)^2 - 2
- Question 5, Exercise 1.4
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder... 3+b^3+c^3-3abc=0$$ $$\implies a^3+b^3+c^3=3abc.$$ Putting values of $a$, $b$ and $c$, we get \begin{al
- Question 1, Exercise 1.1
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder
- Question 2, Exercise 1.1
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder
- Question 3, Exercise 1.1
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder
- Question 5, Exercise 1.1
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder
- Question 6, Exercise 1.1
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder
- Question 7, Exercise 1.1
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder
- Question 1, Exercise 1.2
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder
- Question 2, Exercise 1.2
- nit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Feder