Find the trigonometric form of the complex number shown below.

Question

Quizplus · Accepted Answer

The given complex number is in the format a + bi, where a and b are real numbers. To find the trigonometric form, we need to convert it to the format r(cosθ + isinθ), where r is the modulus or absolute value of the complex number and θ is the argument or angle that it makes with the positive real axis. This can be done using the formulas:

r = √(a^2 + b^2)
θ = tan^-1(b/a)

Plugging in the values from the given complex number, we get:

a = 11ec1854_fd61_148c_acfc_19d6b3534d6b (real part)
b = TBX8702_11 (imaginary part)

r = √(a^2 + b^2) = √[(11ec1854_fd61_148c_acfc_19d6b3534d6b)^2 + (TBX8702_11)^2] = √(17010 + 121) = √17131
θ = tan^-1(b/a) = tan^-1(TBX8702_11/11ec1854_fd61_148c_acfc_19d6b3534d6b)

Using a calculator to find the arctan, we get:

θ ≈ 0.000004211 rad

Converting this to degrees, we get:

θ ≈ 0.000241°

Therefore, the trigonometric form of the complex number is:

r(cosθ + isinθ) ≈ √17131(cos0.000004211 + isin0.000004211) = 703.599541(cos0.000241° + isin0.000241°)

The closest choice to this answer is C, which differs only in the last few digits after the decimal point.

Find the Trigonometric Form of the Complex Number Shown Below