Product of the

Answer to Problem 40E
Theproduct of the complex numbers in trigonometric form is 25(cos400+isin400)
Explanation of Solution
Given info:
z=[12(cos1000+isin1000)][45(cos3000+isin3000)]
Formula used:
Let z1=r1(cosθ1+isinθ1) and z2=r2(cosθ2+isinθ2) we have
z1z2=r1r2(cos(θ1+θ2)+isin(θ1+θ2))z1z2=r1r2(cos(θ1−θ2)+isin(θ1−θ2))
Calculation:
We have
z=[12(cos1000+isin1000)][45(cos3000+isin3000)]z1=r1(cosθ1+isinθ1)=12(cos1000+isin1000)z2=r2(cosθ2+isinθ2)=45(cos3000+isin3000)z=z1z2=r1r2(cos(θ1+θ2)+isin(θ1+θ2))z=12×45(cos(1000+3000)+isin(1000+3000))z=25(cos4000+isin4000)z=25(cos400+isin400)
The product of the complex numbers in trigonometric form is 25(cos400+isin400)
Conclusion:
Thus,theproduct of the complex numbers in trigonometric formis 25(cos400+isin400)
Chapter 6 Solutions
EBK PRECALCULUS W/LIMITS
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