Question

5x-6yi=15-12i how to solve x and y

Answer 1

Since we have two complex numbers equal to each other their magnitudes (absolute value) and arguments should be equal. So from equating absolute values, \[\sqrt{(5x)^2+(6y)^2} = \sqrt{15^2+12^2}\] and from equal arguments \[tan^{-1}(\frac{6y}{5x}) =tan^{-1}(\frac{15}{12})\]So now we have two equations and two variables(x and y), can you solve for their values?

Answer 2

Well assuming \(x,y\in\mathbb{R}\), we can simply equate the real and imaginary parts.\[a_1+b_1i=a_2+b_2i~~\text{with}~~a_1,b_1,1_2,b_2\in\mathbb{R}~\Longleftrightarrow ~a_1=a_2~\text{and}~b_1=b_2\]So \(5x=15\) and \(-6y=-12\).

Do you follow?