Add, subtract, multiply, and simplify expressions in the form a + bi.
A complex number has the form a + bi, where a is the real part and b is the imaginary part, and i = √(−1). The set of complex numbers ℂ contains all real numbers (when b = 0) and all purely imaginary numbers (when a = 0).
(3 + 2i)(1 − 4i) = 3 − 12i + 2i − 8i² = 3 − 10i − 8(−1) = 3 + 8 − 10i = 11 − 10i.
The complex conjugate of a + bi is a − bi. Their product is always real: (a + bi)(a − bi) = a² + b². Use conjugates to divide complex numbers.
Remember This!
To divide complex numbers, multiply both numerator and denominator by the conjugate of the denominator. This eliminates i from the denominator.
What is (2 + 3i)(2 − 3i)?