Homework SourseGiven two complex numbers z1 r1cos 1 i sin 1 and z2 r2cos
Given two complex numbers z1 = r1(cos 1 + i sin 1) and z2 = r2(cos 2 + i sin 2), show that z1 z2 = r1 r2 [cos(1 2) + i sin(1 2)]
Solution
z1 = r1(cos 1 + i sin 1)
and z2 = r2(cos 2 + i sin 2),
Solution : z1*z2 = r1(cos 1 + i sin 1)*r2(cos 2 + i sin 2)
= r1r2[cos1cos2 + icos1sin2 + isin1cos2 -sin1sin2]
=r1r2[(cos1cos2 - sin1sin2) +i(cos1sin2 + sin1cos2)
= r1r2[cos(1 +2) +sin(1 +2)]
Please check .
![Given two complex numbers z1 = r1(cos 1 + i sin 1) and z2 = r2(cos 2 + i sin 2), show that z1 z2 = r1 r2 [cos(1 2) + i sin(1 2)]Solutionz1 = r1(cos 1 + i sin 1)](/WebImages/30/given-two-complex-numbers-z1-r1cos-1-i-sin-1-and-z2-r2cos-1083286-1761569222-0.webp "Given two complex numbers z1 = r1(cos 1 + i sin 1) and z2 = r2(cos 2 + i sin 2), show that z1 z2 = r1 r2 [cos(1 2) + i sin(1 2)]Solutionz1 = r1(cos 1 + i sin 1)")
