Question

Question 10 Express the given complex number in the form a + ib: (-2- i/3)^3

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

Answer 1

(-2 - 1/3i)³
Use, (a + b)³ = a³ + 3a²b+3ab²+b³ here,

(-2 - 1/3i)³ = -(2 + 1/3i)³
= -[(2)³ + 3(2)²(1/3)i+3(2)(1/3i)²+(1/3i)³]
= -[8 + 4i +(2/3)i² - (1/27)i]
=-[8 - 2/3 + 4i - (1/27)i]
=-[(24-2)/3 + (4 - 1/27)i]
= -[22/3 + (107/27)i]
Hence, -[22/3 + (107/27)i] is the answer.