If   then show that |z| = 1.

Let z and ω be two complex numbers such that |z| ≤ 1 and |w| ≤ 1 then show that .

Find all non zero complex numbers satisfying .

Let and  be the roots of the equation  where the coefficients p and q may be complex numbers. Let A and B represent  in the complex plane. If  and OB = OA where O is the origin, prove that .

Let and  are two complex numbers such that  then prove that .

Prove that there exists no complex number z such that  and .

True/False
If the complex numbers  represent the vertices of an equilateral triangle with  then .

a) True

b) False

If three complex numbers are in arithmetic progression then they lie on a circle in the complex plane.

a) True

b) False

For any two complex numbers  and any real numbers  is equal to .  .  .  .

a)  

b)  

c)  

d)  

If a and b are real numbers between 0 and 1 such that the points  form an equilateral triangle then a is equal to .  .  .  .

a)  

b)  

c)  

d)  

a) x = Φ

b) x = 1

c) x = −1

d) x = ± 1

Solve for x
6.2^2x – 13.6^x + 6.3^2x = 0

a) x = Φ

b) x = 1

c) x = −1

d) x = ± 1

Solve for x
 

a) x = 0, 1

b) x = 1, 2

c) x = 2, 3

d) x = 0, 1, 2, 3

Solve for x
5^{2x + 1} + 7^{x + 1} – 175^x – 35 = 0

a) x = Φ

b)

c)

d) , 7

Solve for x
 

a) x = Φ

b) x = 1

c) x = 3

d) all of the above

Solve for x
 

a) x = Φ

b) x = 1

c) x = - 3

d) x = 1, - 3

Solve for x
 

a) x = Φ

b) x = 3

c) x = 6

d) x = 9

Solve for x
 

a) x = Φ

b)

c)

d) , 1

Solve for x
4^{2x – 3} = 7^{x – 1.5}

a) x = 0

b)

c)

d)

Solve for x
9^{x + 2} = (13)^{2x – 1}

a) x = 1

b) x = ln9 + ln13

c)

d)

Solve for x
27^{x – 2/3} – 9^{x – 1}  = 2.3^{2x – 1} – 2.3^{3x – 1}

a) x = 0

b) x = 1

c) x = 2

d) x = 3

Solve for x
4^x + 6^x – 9^x = 0

a) x = 0

b) x = 1

c)

d)

Solve for x
3^{2x + 1} + 8^{x + 1} – (72)^x – 24 = 0

a) x = Φ

b)

c)

d) ,