Question

Find the product of z1 and z2, where z1 = 7(cos 40° + i sin 40°) and z2 = 6(cos 145° + i sin 145°). 42(cos 40° + i sin 40°) 42(cos 185° + i sin 185°) 13(cos 185° + i sin 185°) 42(cos 5800° + i sin 5800°)

Answer 1

`\bf \qquad \textit{ product of two complex numbers}\\\\ r_1[cos(\alpha)+isin(\alpha)]\quad \cdot \quad r_2[cos(\beta)+isin(\beta)] \\\\\\ ~~~~~~~~~r_1\cdot r_2[cos(\alpha + \beta)+isin(\alpha + \beta)]\\\\ -------------------------------\\\\ \stackrel{z1}{7[cos(40^o)+i~sin(40^o)]}~~\cdot ~~\stackrel{z2}{6[cos(145^o)+i~sin(145^o)]} \\\\\\ ~~~~~~~~~7\cdot 6[cos(40^o+145^o)+i~sin(40^o+145^o)] \\\\\\ ~~~~~~~~~42[cos(185^o)+i~sin(185^o)]`