The value of (1+i)^3+(1-i)^6 is (a) 10-2 i (b) 2 (c) ((1-5 i))/(√(2)) (d) -2+10 i

Name: Problem 54, Chapter 1: IIT JEE Super Course in Mathematics ALGEBRA II
Uploaded: 2021-06-05T09:39:54-08:00
Duration: 3 min 59 s
Channel: Anas Venkitta
Description: The value of (1+i)^3+(1-i)^6 is (a) 10-2 i (b) 2 (c) ((1-5 i))/(√(2)) (d) -2+10 i

step 1 So in the given question we are told to find the value of the expression 1 plus i raised to 3 pl

The value of (1+i)^3+(1-i)^6 is (a) 10-2 i (b) 2 (c) ((1-5...

Key Concepts

Complex Numbers

Complex numbers are a set of numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit. They allow for the solution of equations that do not have solutions within the real numbers and are fundamental in various areas of mathematics and engineering.

Imaginary Unit

The imaginary unit, denoted as i, is defined by the property i² = -1. It is a cornerstone of complex number theory, and understanding the cyclical nature of its powers (i, -1, -i, 1, and so on) is essential when performing arithmetic operations involving complex numbers.

Polar Form Representation

Expressing a complex number in polar form involves using its modulus (or absolute value) and its argument (or angle). This representation, typically written as r·(cos? + i·sin?) or r·e^(i?), simplifies the process of raising complex numbers to powers or extracting roots.

De Moivre's Theorem

De Moivre's Theorem provides a straightforward method for raising complex numbers in polar form to integer powers. It states that (r·e^(i?))^n = r^n · e^(i·n?), which transforms exponentiation into simpler operations on the modulus and the argument, facilitating the evaluation and simplification of expressions involving complex powers.

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