Question

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

Answer 1

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

Answer 2

➙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.

$\frac{ - 5i}{ - 5} = \frac{z + 2}{ - 5}$

So the answer is

• $i=−1 \frac{ - 1} 5z+ \frac{ - 2}{5}$