Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Aim: How do we multiply or divide complex numbers? Do Now: 1. Multiply: (3 2 x)( 2 x) 2. Multiply: (3 2 2 )( 2 2 ) 3. Multiply: (3 2i )( 2 i ) 6 + 7x + 2x2 10 7 2 4 + 7i HW: p.216 # 26,30,32,36,38,40,50,52 Multiplying Treat the i’s like variables, then change any i2 to -1 Ex: i (3 i ) 2 3i i 3i ( 1) 1 3i Remember: Ex: ( 2 3i )( 6 2i ) 12 4i 18i 6i 12 22i 6(1) 12 22i 6 6 22i The product of two complex numbers is a complex number 2 Complex Conjugate The conjugate of the complex number a + bi is the complex number a – bi. For example, the conjugate of 5 + 2i is 5 – 2i. Similarly, 3 – i and 3 + i are conjugates to each other. The product of two complex numbers that are conjugates is a real number (5 2i)(5 2i) 25 10i 10i 4i 2 25 4i 25 4 29 2 Divide 8 + i by 2 – i 8i (8 i) (2 i) 2i Write the division problem in fractional form 15 10i 3 2i 5 5 Simplify and write the result in the form of a + bi (8 i)( 2 i) Multiply the conjugate of the denominator, and the numerator (2 i)( 2 i) also multiply accordingly 2 16 10i i Multiply the binomials and 2 combine the like terms 4i 16 10i 1 15 10i Simplify 4 1 5 Write the multiplicative inverse of 2 + 4i in the form of a + bi 1 2 4i 1 (2 4i) (2 4i)( 2 4i) 2 4i 4 8i 8i 16i 2 2 4i 2 4i 2 4 16 4 16i 2 4i 1 1 i 20 10 5 The multiplicative inverse of 2 + 4i Rationalize the denominator by multiplying the conjugate of the denominator on both the numerator and denominator Multiply Simplify: Simplify and write the result in a + bi form 3 11i 1 2i Multiply : 1 2i 1 2i (3 11i )( 1 2i ) (1 2i )( 1 2i ) 3 6i 11i 22i 2 1 2i 2i 4i 2 3 5i 22(1) 1 4(1) 3 5i 22 1 4 25 5i 5 25 5i 5 5 5 i Drill: 1. Multiply: (7 i )(1 2i ) 5 – 15i 2. Multiply: (3 – 2i)(3+2i) 13 3. Divide: (3 12i ) 3i 4. Multiply: (4 i ) (3 49 )( 2 16 ) 5. Write the multiplicative inverse of 9 – 2i and then simplify: 34 – 2i 9 2 i 85 85