DIVIDING COMPLEX NUMBERS

DO NOW Today’s Objective IWBAT multiply and divide complex numbers... And Why To work with the square roots of negative numbers 3. ( 3-2i) + (-5-9i) 4. (2 - 5i) - (-1 - 6i) -2i - 8i 2 -2i -8(-1) = -2i i +2i -7i i + 7 = i i 3 + 1i

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: – 5i 8 + i 9i

3 - 2i3 + 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:

What happens if you multiply conjugates??? Important: The product of two complex conjugates is always a real number.

STEP 4:

DIVIDE

Example # i = i -10i -4(-1) i = i = Step4. Step 3: Step 2: Step 1: Step 5: i 29 29

Example #4 Find the quotient (5+2i) and (4 - 3i) or

Exit ticket answer key