If z = x + iy, find the following in rectangular form.
\(Re\left( \frac { 1 }{ z } \right) \)

Represent the complex number −1−i

Write the following in the rectangular form:
\(\cfrac { 10-5i }{ 6+2i } \)

Find the square roots of −6+8i

Obtain the Cartesian form of the locus of z = x + iy in each of the following cases:
\(\overline { z } =z^{ -1 }\)

Show that the following equations represent a circle, and, find its centre and radius
|3z-6+12i| = 8

Write in polar form of the following complex numbers
\(3-i\sqrt { 3 } \)

Simplify the following:
i i²i³...i⁴⁰

Find the modulus and principal argument of the following complex numbers.
\(-\sqrt { 3 } +i\)

Represent the complex numbe \(1+i\sqrt { 3 } \) in polar form.

Find Re (z) and im (z) if z = 5i¹¹ + 7i³

If (cosθ + i sinθ)² = x + iy, then show that x²+y² =1

If 1, ω, ω² are the cube roots of unity show that (1+ω²)³ - (1+ω)³ = 0

Find the argument of -2

Find the values of the real number x and y if 3x + (2x - 3y) i = 6 + 3i⁹.