Answer :

It is given in the question that,

=

=

=

=

=

= [- 1 – i]^{3}

= (- 1)^{3} [1 + i]^{3}

= - [1^{3} + i^{3} + 3 × 1 × i (1 + i)]

= - [1 + i^{3} + 3i + 3i^{2}]

= - [1 – i + 3i – 3]

= - [- 2 + 2i]

**= 2 – 2i**

Rate this question :

If z and w are two complex numbers such that |zw| = 1 and arg (z) – arg (w) = π/2, then show that

Mathematics - ExemplarState True of False for the following:

The inequality |z – 4| < |z – 2| represents the region given by x > 3.

Mathematics - ExemplarState True of False for the following:

If z is a complex number such that z ≠ 0 and Re (z) = 0, then Im (z^{2}) = 0.

State True of False for the following:

The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).

Mathematics - ExemplarSolve for x: (1 – i) x + (1 + i) y = 1 – 3i.

RS Aggarwal - MathematicsFind the real value of a for which 3i^{3} – 3ai^{2} + (1 – a) i + 5 is real.

If n ∈ N, then find the value of i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3}.

Write the least positive integral value of n for which is real.

RD Sharma - MathematicsIf find the value of x^{2} + y^{2}.

If n is any positive integer, write the value of

RD Sharma - Mathematics