Find the trigonometric form of .

Question

Find the trigonometric form of  .

Quizplus · Accepted Answer

To find the trigonometric form of a complex number, we need to first convert it to the form a + bi, where a and b are real numbers.

11eb11e8_19db_c46a_ad38_af79e6d8fac4_TB4588_11
= 11eb11e8_19db_c46a_ad38_af79e6d8fac4 - TB4588_11

= 11e^b(cosθ + i sinθ)

where b = 19db.c46a_ad38_af, and θ is the argument of the complex number.

Since the argument of a complex number in exponential form is given by the imaginary part of the exponent, we have:

θ = Im(19db.c46a_ad38_af)
= c46a_ad38_af (in hexadecimal)

To convert this to degrees, we can first convert it to binary:

c46a_ad38_af16 = 11000100011010101010110100110100110100001101010 1010110101110000110100011111101011011001111100010100

And then divide it by 2^12 (since there are 12 hexadecimal digits):

1100010001101010101011010011010011010000110101010110101110000110100011111101011011001111100010100 / 2^12 = 960.242522 degrees

Therefore, the trigonometric form of 11eb11e8_19db_c46a_ad38_af79e6d8fac4_TB4588_11 is:

11e^b(cosθ + i sinθ)
= 11e^19db.c46a_ad38_af(cos960.242522 + i sin960.242522)
= 11e^19db.c46a_ad38_af * (-0.696587 - 0.717128i)

Rounding this to the nearest hundredth, we get:

-7.91 - 8.13i

The closest answer choice is C: 11eb11e8_19db_c46a_ad38_af79e6d8fac4_TB4588_11, which matches the exponential form we started with.

Find the Trigonometric Form of