Find the modulus and the arguments of each of the complex numbers in

NCERT Miscellaneous Exercise Question 14. Find the real numbers x and y if {\displaystyle (x-iy)(3+5i) } is the conjugate of {\displaystyle -6-24i } .

NCERT Chapter 5 Complex Numbers Example 12 Find the conjugate of {\displaystyle \frac{(3-2i)(2+3i)}{(1+2i)(2-i)} }

NCERT Exercise 1.5 Question 5: Draw appropriate Venn diagram for each of the following:
(i) (A ∪ B)′,
(ii) A′ ∩ B′,
(iii)  (A ∩ B)′,
(iv) A′ ∪ B′

Sequences and Series Class 11 Maths Example 23: If a, b, c, d and p are different real numbers such that {\displaystyle (a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2) \le 0 } , then show that a, b, c and d are in G.P.

Sequences and Series NCERT Exercise 9.3 Question 24 Class 11 Maths : Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from {\displaystyle (n+1)^{th} \text{ to } (2n)^{th} } term is {\displaystyle \frac{1}{r^n} } .

NCERT Exemplar Class 11 Maths Chapter 3 Trigonometry Functions Example 4 If θ lies in the second quadrant, then show that { \displaystyle \sqrt{\frac{1-\sin\theta}{1+\sin\theta}} + \sqrt{\frac{1+\sin\theta}{1-\sin\theta}} = -2 \sec\theta }

NCERT Exemplar Class 11 Maths Chapter 3 Trigonometry Functions Example 3 Find the value of { \displaystyle \sqrt{3} \text{cosec} 20^\circ – \sec 20^\circ }

NCERT Exemplar Class 11 Maths Chapter 3 Trigonometry Functions Example 2 If { \displaystyle A = cos^2 θ + sin^4 θ } for all values of θ, then prove that { \displaystyle \frac{3}{4} \le A \le 1} .

NCERT Exemplar Class 11 Maths Chapter 3 Trigonometry Functions Example 1 A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.

NCERT Exemplar Class 11 Maths Chapter 3 Trigonometry Functions Example 6: Prove that { \displaystyle \frac{sec8\theta-1}{sec4\theta-1}=\frac{tan8\theta}{tan2\theta}}

NCERT Exemplar Class 11 Maths Chapter 3 Trigonometry Functions Example 5: Find the value of tan9°–tan27°–tan63°+tan81°