Complex Numbers & Operations
Master the fundamentals of complex numbers, imaginary unit i, and arithmetic operations.
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Questions Covered in This Set
10 cards to master
What is the definition of the imaginary unit i?
i² = -1, or equivalently i = √(-1)
What is the standard form of a complex number?
a + bi, where a is the real part and b is the imaginary part
How do you add two complex numbers (a + bi) + (c + di)?
Combine like terms: (a + c) + (b + d)i
What is the complex conjugate of a + bi?
a - bi (flip the sign of the imaginary part)
What is the result of multiplying a complex number by its conjugate (a + bi)(a - bi)?
a² + b², which is always a real number
What is the cycle pattern for powers of i?
i, -1, -i, 1, then repeats every 4th power
What is i³ equal to?
-i
How do you divide complex numbers?
Multiply both numerator and denominator by the conjugate of the denominator
Calculate: (3 + 2i) + (1 - 5i)
4 - 3i
What is i⁴ equal to?
1
