Question

Convert 4+3i into polar form

Answer 1

Answer:

4 - 3i means you've gone 4 right and 3 down from the origin. That makes a right triangle with two legs of lengths 3 and 4 and a hypotenuse of length of r (the length of the vector from the origin to (4, -3)). Solve for r using the Pythagorean Theorem:

c2 = a2 + b2

r2 = 32 + 42

r2 = 9 + 16

r2 = 25

r = 5

Now, let's find the value of θ, the angle described by that vector. Since θ is in Quadrant IV, tangent will be negative.

tan(θ) = opposite/adjacent = -3/4

θ = tan-1(3/4) = -36.9°

That's not between 0 and 360, so add 360 to find an equivalent angle:

θ = -36.9° + 360° = 323.1°

One way to write this in Polar Form is 5 ∠323.1°.

Step-by-step explanation:

Answer 2

Answer:

4 - 3i means you've gone 4 right and 3 down from the origin. That makes a right triangle with two legs of lengths 3 and 4 and a hypotenuse of length of r (the length of the vector from the origin to (4, -3)). Solve for r using the Pythagorean Theorem:

c2 = a2 + b2

r2 = 32 + 42

r2 = 9 + 16

r2 = 25

r = 5

Now, let's find the value of θ, the angle described by that vector. Since θ is in Quadrant IV, tangent will be negative.

tan(θ) = opposite/adjacent = -3/4

θ = tan-1(3/4) = -36.9°

That's not between 0 and 360, so add 360 to find an equivalent angle:

θ = -36.9° + 360° = 323.1°

One way to write this in Polar Form is 5 ∠323.1°.