In the complex plane, the rectangular coordinates (x, y) represent a complex number. Which statement explains why polar coordinates (r, θ) represent the same complex number?

Option (2)

Step-by-step explanation:

From the picture attached,

Let the rectangular coordinates (x, y) is represented by the polar coordinates (r, θ).

By applying Pythagoras theorem in ΔPAO,

PO² = AO² + AP²

r² = x² + y²

r =

By applying tangent rule in ΔAPO,

tanθ =

tanθ =

θ =

Therefore, Option 2 will be the correct option.

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

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step-by-step explanation: