Answer:
[tex]Z_{1} Z_{2} = 3 i[/tex]
Step-by-step explanation:
Step(i):-
Given z 1 = 3(cos 37° + i sin 37°)
z 2 = (cos 53° + i sin 53°)
by using complex numbers
[tex]Z_{1} = r_{1} ( cos\alpha_{1} + isin\alpha_{1} ) = r_{1} cis\alpha _{1}[/tex]
[tex]Z_{2} = r_{2} ( cos\alpha_{2} + isin\alpha_{2} ) = r_{2} cis\alpha _{2}[/tex]
step(ii):-
now
[tex]Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})[/tex]
z ₁ = 3(cos 37° + i sin 37°) = 3 c i s 37°
z ₂ = (cos 53° + i sin 53°) = c i s 53°
we will use formula
[tex]Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})[/tex]
[tex]Z_{1} Z_{2} = 3 X 1 cis (37 + 53) = 3cis (90) = 3 cis(\frac{\pi }{2} )[/tex]
[tex]Z_{1} Z_{2} = 3(cos(\frac{\pi }{2} ) + isin(\frac{\pi }{2}))[/tex]
[tex]Z_{1} Z_{2} = 3(0 + i (1)) = 3 i[/tex]
Conclusion:-
[tex]Z_{1} Z_{2} = 3 i[/tex]
Answer:
2i
Step-by-step explanation:
z 2 = 2/3(cos53° + isin53°
I got it right on odyssey ware
