Find all complex numbers such that is a real number.
My Self Assessment
a) z = 2 – 2y + iy, y ε ℝ
.
Solve the equation |z| + z = 3 + 4i
Solve the equation iz2 + (1 + 2i) z + 1 = 0
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
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
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 equation of a circle whose radius and centre are r and respectively, is
a)
b)
c)
d) none of these
The area of the triangle whose vertices are represented by the complex numbers 0, z, zeiα (o < α < π) is equal to
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
Given that 1 + 2i is one root of the equation . Find the other three roots.
