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Identify the Standard Form of a Complex Number - High School Math Question
Mathematics
Grade 11 (Senior High School)
Question Content
Which of these is the standard form for a complex number? Options: A. √-1, B. -1, C. a + bi, D. i
Correct Answer
C
Detailed Solution Steps
1
Step 1: Recall the definition of the standard form of a complex number. A complex number is a number that can be expressed as a combination of a real part and an imaginary part.
2
Step 2: Analyze each option: Option A (√-1) is equal to i, which is just the imaginary unit, not the standard form of a general complex number. Option B (-1) is a pure real number, a subset of complex numbers but not the standard general form. Option D (i) is the imaginary unit, only representing a complex number with a 0 real part and 1 imaginary part, not the general standard form. Option C (a + bi) has a as the real part and b as the coefficient of the imaginary unit i, which fits the definition of the standard form of any complex number, where a and b are real numbers and i is the imaginary unit (i=√-1).
Knowledge Points Involved
1
Standard Form of a Complex Number
The standard form of a complex number is defined as a + bi, where a is the real part, b is the coefficient of the imaginary part, and i is the imaginary unit with the property i² = -1. This form can represent all complex numbers: when b=0, it represents a real number; when a=0 and b≠0, it represents a pure imaginary number.
2
Imaginary Unit i
The imaginary unit i is defined as √-1, which is used to represent the square root of negative numbers. It is the foundation of complex number systems, allowing mathematical operations on numbers that cannot be represented on the real number line.
3
Classification of Complex Numbers
Complex numbers include real numbers (when the imaginary part coefficient b=0 in a+bi) and pure imaginary numbers (when the real part a=0 and b≠0 in a+bi). All real numbers are a subset of complex numbers.
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