Write the coordinate point −2 + 2i in polar form.

(2, 135° )

Step-by-step explanation:

To convert from rectangular to polar form, that is

(x, y ) → (r, Θ ), with

r =

tanΘ =

Given - 2 + 2i, then

r = = = = 2

Since - 2 + 2i is in the second quadrant then Θ must be in the second quadrant.

tanΘ = = - 1, thus

Θ = (- 1) = - 45°, hence

Θ = 180° - 45° = 135° ← in second quadrant

Thus

- 2 + 2i → (2, 135° )

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: