Convert into polar form of 4+3i
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COMPLEX NUMBERS POLAR FORMS DEGREES ARGUMENT THETA
Vianne R. asked • 05/18/15
Write the complex number in polar form
4-3i
Express in 0 less than theta less than 360
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Stephanie M. answered • 05/18/15
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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:
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°.