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DIVIDING COMPLEX NUMBERS DO NOW 8i2 -2i -2i -8(-1) = -2i + 8 3. (3-2i) + (-5-9i) -2 -11i -10 + 35i +2i -7i2 -10 + 37i + 7 = -3 + 37i 4. (2 - 5i) - (-1 - 6i) 3 + 1i Today’s Objective IWBAT multiply and divide complex numbers . . . And Why To work with the square roots of negative numbers Dividing Complex Numbers When we divide, we need to find the Conjugate. The complex numbers & are called complex conjugates (They are EXACTLY the same except for the + or -) TRY THESE: 1. -6 + 5i 2. -6 – 5i 8 – i 8+i 3. -9i 9i 3 + 2i 3 - 2i Dividing Complex Numbers To divide you must clear the denominator of all i’s (called “rationalizing”) To rationalize, multiply the numerator and denominator by the conjugate of the denominator Quotient = Divide Example 1: Important: What happens if The product of two you multiply complex conjugates is conjugates??? always a real number. STEP 4: DIVIDE 6 5 – 2i Example #3 6 5 – 2i Step 1: Step 2: Step 3: Step4. 6(5 + 2i ) (5 – 2i )(5 + 2i ) 5 + 2i 5 + 2i = 30 + 12i = 25 +10i -10i -4(-1)2 30 + 12i 25 +4 = 30 + 12i 29 30 + 12 i 2 25 + 10 i – 10 i – 4i Step 5: 30 + 12i 29 29 Example #4 Find the quotient (5+2i) and (4 - 3i) 5 + 2i 4 – 3i 5 + 2 i 4 + 3i 4 – 3 i 4 + 3i (5 + 2i )(4 + 3i ) (4 – 3i )(4 + 3i ) 2 20 + 15 i + 8 i + 6 i 2 16 – 12 i + 12 i – 9 i 20 + 23 i – 6 14 + 23 i or = 16 + 9 25 14 + 23 i 25 25 Exit ticket answer key