LAST TIME REVISION - XI

TEST- 7/10/25

1) Simplify: 1+ i²+ i⁴+ i⁶.    

2) Write in the form of a + ib where √-1= i

a) √-144 + √441.         

b) √-27 x √12 - √-125 x √-5.     

3) Find the conjugate of (2+ 3i)².      

4) Find x and y if (3x -7) + 5iy = 2y +3 - 4(1- x)i.    

5) Find the modulus of the complex number -12 + 5i.     

6) Express the reciprocal of the complex number 3+ i √5 in the form a+ ib.    

 25/9/25

TRIGONOMETRIC FUNCTIONS 

1) If cotA= 3/4, Find the value of 3 cosA + 5 sinA, where A lies in the first quadrant.   

2) if cos120°= -1/2, find the value of sin120° and tan 120°.    

3) prove that sec(-1680°). sin 330== -1.

4) If A, B, C, D are the angles of the cyclic quadrilateral, show that cosA + cosB + cosC + cosD= 0.    

5) If tan25°= a, prove that (tan155° - tan115°)/(1+ tan155° tan115°)= (1- a²)/2a.

6) If A, B, C be the angles of a triangle, show that 

{Sin(B+ C)+ sin(C+ A)+ sin(A + B)}/{sin(π+ A)+ sin(3π+B)+ sin(5π+ C)}= -1

7) prove that  cosx/(1- sinx) + (1- sinx)/cosx = 2 secx.

8) If secx =√2 and 3π/2< x < 2π, find the value of 

(1+ tanx + cosecx)/(1+ cotx - cosecx).   

23/9/25

COMPLEX NUMBERS 

1) Simplify:

a) i³⁸.          

b) i¹⁵.       

c) i⁻⁶.        

d) 1/i.        

e) (5i) × 7.       

f) (3i)(4i).     

g) 21/14i.        

h) 5/i³.           

i) √-9 + √-16.      

j) (21/4) √-48 - 5 √-27.      

k) √-18 . √-2.           

l) 20/√-5.           

2) Write the complex numbers that represent the following points in the plane.

a) (3,4).     

b) (0,3).     

c) (-1/3,-1/5).     

Also, represent their conjugates.

3) Find the real numbers x and y if (x - iy)(3+ 5i) is the conjugate of -6 - 24i.   

4) Find the modulus of 

a) 5 - 12i³.         

b) (1+ i)/(1- i)  - (1- i)/(1+ i).        

c) (2+ 3i)/(3+ 2i).           

d) (2+ 5i)(3+ 4i).          

e) {(3+ 2i)(1+ i)(2+ 3i)}/{(3+ 4i)(4+ 5i)}.     

5) Find the solution of the equation 

|1- i)|ˣ= 2ˣ.        

6) Show that the points representing the complex numbers (3+ 3i),(--3 -3i) and (-3√3+ 3√3 i) on the Argand plane are the vertices of an equilateral triangle.

7) Express in the standard form a+ ib

a) 1/(3- 8i).            

b) (3+ i)/(+5- 4i).     

c) (1+ i)/(1- i).        

d) {(1- i)/(1+ i)}²      

e) {(1- i)/(1+ i)}³.     

8) Show that the representative points of the complex numbers 1+ 4i, 2+ 7i, 3 + 10i are collinear.

9) if x + iy= √{(a + ib)/(c + id)} then show that (x²+ y²)²= (a²+ b²)/(c²+ d²).