Problem 10 - Algebra and Trigonometry Real Mathematics, Real People

Question

Find real numbers \(a\) and \(b\) such that the equation is true. $$(a+6)+2 b i=6-5 i$$

Step-by-Step Solution

Answer

The values are \(a = 0\) and \(b = -5/2\).

Step 1: Isolate and equate the real parts

Set the real parts equal to each other => \(a + 6 = 6\). Solve this equation for \(a\). The solution is \(a = 0\).

Step 2: Isolate and equate the imaginary parts

Set the imaginary parts equal to each other => \(2b = -5\). Solve this equation for \(b\). The solution is \(b = -5/2\).

Step 3: Result

The solutions for \(a\) and \(b\) are as follows: \(a=0\) and \(b=-5/2\)