Question

This is a precalculus problem on complex numbers. Please give a explanation with your answer, thank you.

Answer 1

➙Let's solve for i.

z=−2−5i

➙Step 1: Flip the equation.

−5i−2=z

➙Step 2: Add 2 to both sides.

−5i−2+2=z+2

−5i=z+2

➙Step 3: Divide both sides by -5.

`( - 5i)/( - 5) = (z + 2)/( - 5)`

So the answer is

• 
  `i=−1 \frac{ - 1} 5z+ ( - 2)/(5)`

Answer 2

`z = \stackrel{x}{-2}\stackrel{y}{-5} i\qquad \begin{cases} \theta =tan^(-1)\left( (y)/(x) \right)\\\\ \theta =tan^(-1)\left( (-5)/(-2) \right)\\\\ \theta \approx 1.19~radians \end{cases}`