Pre Calculus

Question

1) Find the quotient of the complex numbers
2(times)(square root of) 3 (cos (116 (degrees))+ i sin (116(degrees))) / 2 (cos(82(degrees)) + i sin (82 (degrees)))

2) RE write the complex in polar form
z = r(cos (theta) + i sin (theta))
z = 2 - 2 i 

Answer 1

Numerator: 2√3 (cis 116^o)

Denominator: 2 (cis 82^o)

 

quotient: √3 cis (116-82)^o = √3 cis (34^o) -- the "r" factors preceding (cos θ+isinθ), which I abbreviate as cisθ, are divided, and the angles in the "cis" notation are subtracted.

 

FINAL ANSWER: √3 (cos 34^o + i sin 34^o).

 

Second problem: this complex number is located at (2,-2) in the 4th quadrant of the Complex Plane, so the angle is 315^o

and the modulus is 2√2. 

Z = 2√2 (cos 315^o = i sin 315^o)