Solve the equation |z| + z = 3 + 4i

Solve the equation iz² + (1 + 2i) z + 1 = 0

Find all complex numbers such that  is a real number.

Let z₁, z₂  ℂ be complex numbers such that  and . Compute

Find all positive integer n such that  

Let n > 2 be an integer. Find the number of solutions to the equation

Let z₁, z₂, z₃ be complex numbers such that  +  +  = 0 and . Prove that

If  and  are roots of the equation , compute  

If  and  are roots of the equation , compute  

Factorize (in linear polynomials) the polynomial x⁴ + 16

Factorize (in linear polynomials) the polynomial x³ – 27

Factorize (in linear polynomials) the polynomial x⁴ + x² + 1

Find all quadratic equations with real coefficients that have one of the root  

Find all quadratic equations with real coefficients that have one of the root  

Find all quadratic equations with real coefficients that have one of the root

Solve the equation

Compute  when  

Find the number of ordered pairs such that  

Find all real numbers m for which the equation   has at least one real root.

The area of the triangle whose vertices are represented by the complex numbers 0, z, ze^iα (o < α < π) is equal to

a)

b)

c)

d)

The number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals

a) 0

b) 1

c) 2

d) ∞

If  then the maximum value of |z| is equal to

a)

b)

c) 2

d)

Given that 1 + 2i is one root of the equation . Find the other three roots.