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Slide 2 Adapted from Walch Eduation Slide 3 4.3.4: Dividing Complex Numbers 2 Any powers of i should be simplified before dividing complex numbers. After simplifying any powers of i, rewrite the division of two complex numbers in the form a + bi as a fraction. Slide 4 4.3.4: Dividing Complex Numbers 3 Rationalize the denominator of a complex fraction by using multiplication to remove the imaginary unit i from the denominator. The product of a complex number and its conjugate is a real number, which does not contain i. Multiply both the numerator and denominator of the fraction by the complex number in the denominator. Simplify the rationalized fraction to find the result of the division. Slide 5 4.3.4: Dividing Complex Numbers 4 Find the result of (10 + 6i ) (2 i ). Slide 6 4.3.4: Dividing Complex Numbers 5 Rewrite the expression as a fraction. Find the complex conjugate of the denominator. The complex conjugate of a bi is a + bi, so the complex conjugate of 2 i is 2 + i. Slide 7 4.3.4: Dividing Complex Numbers 6 Rationalize the fraction by multiplying both the numerator and denominator by the complex conjugate of the denominator. Slide 8 4.3.4: Dividing Complex Numbers 7 The answer can be left as a fraction, or simplified by dividing both terms in the numerator by the quantity in the denominator. Slide 9 4.3.4: Dividing Complex Numbers 8 Find the result of (4 4i) (3 4i 3 ). Slide 10 ~ms. dambreville