Question

complex numbers

son a) Express Z as a complex number in rectangular form. Z = (5 + 12j).(12 + 5j). e 10 b) Express Z as a complex number in polar form. 2+2+2245° 2=2-2j c) Solve for R and L, where R and L are both real numbers: 200296 + 100Li 102360R

Answer 1

(a) Z = (5+12j)(12+5j)ej10$\pi$ = (169j)*(cos(10$\pi$) + jsin(10$\pi$)) = 169j = 0 + 169j

(b) Z = $\frac{2+2j}{2-2j}$ + 2$\angle 45^{o}$ = $\frac{8j}{8}$ + 2(cos(45o) + jsin(45o)) = j +$\sqrt{2}$ + j$\sqrt{2}$ = $\sqrt{2}$ + j(1+$\sqrt{2}$) = 2.7979$\angle 59.6388^{o}$

(c) $\frac{200\angle 96^{o}}{10\angle 36^{o}}$ = 20$\angle 60^{o}$ = 20(cos(60o) + jsin(60o)) = 10 + j17.3205

thus R = 10

L = 17.3205/100 = 0.173205