1. Section 2.4 – The Complex Numbers

2. The Complex Number i Express the number in terms of i.

3. Def: A complex number is of the form a + bi, where a and b are real numbers. a is the real part of the complex number and bi is the imaginary part. When a = 0, the number is called pure imaginary. When b = 0, the number is real. Ex: 2 – 3i is a complex number. 2 is the real part, -3i is the imaginary part. Complex Numbers a + bi 4i - 6 is not in standard form. -6 + 4i is in standard form.

4. Addition and Subtraction ***Complex numbers follow the commutative, associative and distributive properties. Add and subtract just like you would real binomials.

5. Multiplication of Complex Numbers

6. ***When multiplying, you must replace the negative under the radical with an i on the outside first. Ex.

7. Division of Complex Numbers The conjugate of a complex number a + bi is a – bi. The product of a complex number and its conjugate is a real number. ***When dividing complex numbers, we multiply the numerator and denominator by the complex conjugate of the denominator.

8. Division of Complex Numbers Ex.

9. Simplifying Powers of i When the exponent is divided by 4, the remainder gives the the equivalent power of i. Ex.