complexnumbers

The number √(-1) is called: Complex number

(-1)¹⁹ = -1

(-1)^(−21/2) = -i

Multiplicative inverse of (0, -1) = (0, 1)

Multiplicative inverse of -i = i

Real part of 3/(√6 − √(-12)) = (√6)/6

Any real number ‘a’ is equal to: (a, 0)

Real part of (1 + 3i)/(2i) = 3/2

Modulus of -5i = 5

If z = -2 + 3i, then conjugate = -2 - 3i

a² + b² factors as: (a + ib)(a − ib)

(0, 1) × i = (-1, 0)

If Z = -7 - 24i, real part of √Z × i = -4

If ω is a cube root of unity, (3 + ω)(3 + ω²) = 7

Complex cube roots of -1 are: -1, -ω, -ω²

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Targets: Target 1: Concept mastery in complex arithmetic
Target 2: Competitive exam accuracy improvement
Target 3: Advanced algebraic problem-solving speed

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