Which of the following complex numbers is located in the third quadrant when gra

Question

Which of the following complex numbers is located in the third quadrant when graphed in the complex plane? 5(cos 75 degree + i sin 75 degree) cos 269 degree + i sin 269 degree 2 (cos 290 degree + i sin 290 degree) 10(cos 179 degree + i sin 179 degree) Find (2(cos 35 degree + i sin 35 degree))5 using DeMoivre's theorem. 10(cos 185 degree + i sin 185 degree) 32(cos 175 degree + i sin 175 degree) 32(cos 40 degree + i sin 40 degree) 25(cos 175 degree + i sin 175 degree) Find the fourth roots of -64. Which of the following is Dot one of them? 2 (cos315 degree +i sin315 degree) 2 (cos45 degree + i sin 45 degree) 2 (cos 215 degree + i sin 215 degree) 2 (cos135 degree + i sin135 degree)

Explanation / Answer

Here we need to place the complex number in complex plane. In third quadrant both coordinates should be negative. Hence option B will be correct answer.

cos 269 + i sin 269

we convert it in first complex number form x+i y

standard polar form is r(cos ? + i sin ?)

here r = 1, ? = 269

x = rcos ? = 1 * cos 269 = -0.017

y = rsin ? = 1 * sin 269 = -0.999

Here both x and y are negative. Hence we will locate it in third quadrant.

Option B is correct answer.

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