Math Problem Statement

The value of i (iota) in the complex number set is ... (a) -1 (b) 1 (c) (0,1) (d) (1,0)

Solution

The question is asking for the value of ii (iota) in the complex number set. In complex numbers, ii represents the imaginary unit, which is defined by the property that i2=1i^2 = -1.

This implies that the value of ii itself is:

  1. Not a real number.
  2. Represented as (0,1)(0, 1) in ordered pair form, where 00 is the real part and 11 is the imaginary part.

Thus, the correct answer is:

(c) (0,1)(0, 1).

Would you like further details on complex numbers or how to interpret ordered pairs in the complex plane?

Here are some related questions that expand on this concept:

  1. What does i2=1i^2 = -1 signify in complex numbers?
  2. How are complex numbers represented in the form a+bia + bi?
  3. What is the significance of the real and imaginary parts of a complex number?
  4. How can we visualize complex numbers on the complex plane?
  5. What are the powers of ii and how do they cycle?

Tip: In complex numbers, the real part of ii is 0, and the imaginary part is 1. This makes its representation as an ordered pair easy to interpret: (0,1)(0, 1) corresponds to ii in the complex plane.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Imaginary Unit
Complex Plane

Formulas

i^2 = -1

Theorems

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Suitable Grade Level

Grades 9-10