How do I work the following problem? I cannot find an example in my book that shows how to divide when there are two variables on top.
4-2i/7+3i
Thanks for your help today.
you have to combine the like variables
To divide expressions with two variables on top, we will use the conjugate of the denominator. In this case, the denominator is 7+3i. The conjugate of 7+3i is 7-3i.
To divide the given expression (4-2i) by (7+3i), follow these steps:
Step 1: Multiply the numerator and denominator by the conjugate of the denominator.
(4-2i) * (7-3i) / (7+3i) * (7-3i)
Step 2: Simplify the expression in the numerator using the distributive property.
(4*7 + 4*(-3i) - 2i*7 - 2i*(-3i)) / (7*7 + 7*(-3i) + 3i*7 + 3i*(-3i))
Step 3: Simplify each term in the numerator.
(28 - 12i - 14i + 6i^2) / (49 - 21i + 21i - 9i^2)
Note: i^2 equals -1.
Step 4: Combine like terms in the numerator.
(28 - 26i + 6(-1)) / (49 - (-9))
Step 5: Simplify further.
(28 - 26i - 6) / (49 + 9)
(22 - 26i) / 58
Step 6: Simplify the final expression if possible.
We can divide both the numerator and denominator by their greatest common factor, which is 2.
(11 - 13i) / 29
So, the simplified expression is (11 - 13i) / 29.