If z₁ and z₂ are two complex numbers, such that |z₁| = Iz₂|, then is it necessary that z₁ = z₂?

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

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

If z₁ and z₂ are 1-i, -2+4i then find Im\(\left( \frac { { z }_{ 1 }{ z }_{ 2 } }{ \bar { { z }_{ 1 } } } \right) \).

If z =\(\left( \frac { \sqrt { 3 } }{ 2 } +\frac { i }{ 2 } \right) ^{ 107 }+\left( \frac { \sqrt { 3 } }{ 2 } -\frac { i }{ 2 } \right) ^{ 107 }\), then show that Im (z) = 0

Find the value of the complex number (i²⁵)³.

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 modules of (1+ 3i)³

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

Find the value of \(i^{57}+\frac{1}{i^{125}}\)

Evaluate 
(i) i⁴ⁿ⁺¹
(ii) i³+i^-3

Simplify: \(\frac{1}{i}-\frac{i}{i^{2}}+\frac{1}{i^{3}}-\frac{1}{i^{4}}\)

Simplify \(i^{2}+i^{4}+i^{6}+\ldots(2 n+1)\) terms.

Find the values of x and y if 4x+ i(3x-y) = 3 - 6i