Working with imaginary numbers and complex operations
What is i² equal to?
By definition, i is the imaginary unit where i² = -1
Simplify: (3 + 2i) + (1 - 4i)
Add real parts and imaginary parts separately
Multiply: (2 + i)(3 - 2i)
Use FOIL: 6 - 4i + 3i - 2i² = 6 - i - 2(-1) = 6 - i + 2 = 8 - i
What is the complex conjugate of 5 - 3i?
Complex conjugate changes the sign of the imaginary part
Divide: (4 + 2i)/(1 + i)
Multiply numerator and denominator by conjugate of denominator