Question

Question 9 Express the given complex number in the form a + ib: (1/3 + 3i)^3

Class X1 - Maths -Complex Numbers and Quadratic Equations Page 104

Answer 1

(1/3 + 3i)³
use, (a + b)³ = a³ + 3a²b+3ab²+b³

(1/3 + 3i)³ = (1/3)³ + 3(1/3)²(3i)+3(1/3)(3i)² + (3i)³
= 1/27 + i + 9i² + 27i³
= 1/27 + i -9 -27i [ use, i² = -1, i³=-i]
= (1 -243)/27 + (1 - 27)i
= (-242)/27 -26i
Hence, (-242/27) -26i is the answer .