Algebraic Form of a Complex Number
A complex number is z = x + iy with x, y real and i2 = -1; x is the real part and y the imaginary part.
What is Algebraic Form of a Complex Number?
A complex number is z = x + iy with x, y real and i2 = -1; x is the real part and y the imaginary part.
Key formula / rule: Equality of two complex numbers means equality of real and imaginary parts separately.
Key points
- Define a complex number and identify its real and imaginary parts.
- Compute sums, products and quotients of complex numbers in algebraic form.
Common exam trap
Treating i as a real quantity and writing √(-4)*√(-9) = √(36).
Definitions
- Term
Algebraic Form of a Complex Number
- Meaning
A complex number is z = x + iy with x, y real and i2 = -1; x is the real part and y the imaginary part.
- Term
Algebraic Form of a Complex Number — explanation
- Meaning
Real numbers cannot solve x2 + 1 = 0, so the field is extended by the symbol i. Every algebraic operation on complex numbers follows the ordinary rules of algebra with the single extra rule i2 = -1, which is why the set is closed under addition, multiplication and division by a non-zero element.
Learning objectives
Define a complex number and identify its real and imaginary parts.
Compute sums, products and quotients of complex numbers in algebraic form.
Formulae
- Key point
Equality of two complex numbers means equality of real and imaginary parts separately.
- Key point
Powers of i repeat with period 4: i, -1, -i, 1.
- Key point
Division is performed by multiplying numerator and denominator by the conjugate.
Common mistakes
Treating i as a real quantity and writing √(-4)*√(-9) = √(36).
Comparing two complex numbers with < or >, which is undefined.
Keywords
Algebraic
Form
Complex
Number
Practice preview
What is the real part of the complex number z = 7 - 3i?…
easy
Simplify the expression: (5 + 2i) + (3 - 4i).…
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If (x + 2) + (y - 1)i = 4 + 3i, what are the values of x and y?…
easy