Find the product of the complex numbers \(\displaystyle{z}_{{{1}}}={4}{\left({{\cos{{50}}}^{{\circ}}+}{i}{\sin{{50}}}^{{\circ}}\right)}\) and

Karla Thompson

Karla Thompson

Answered question

2022-04-07

Find the product of the complex numbers
z1=4(cos50+isin50)
andz2=7(cos100+isin100)
Leave the answer in polar form.

Answer & Explanation

tutaonana223a

tutaonana223a

Beginner2022-04-08Added 15 answers

Step 1
Given complex numbers
1) z1=4(cos50+isin50)
2) z2=7(cos100+isin100)
Multiplying both the complex numbers
z1×z2=[4(cos50+isin50)]×[7(cos100+isin100)]
z1×z2=28{cos50+isin50)(cos100+isin100)
z1×z2=28(cos50cos100+isin100cos50+isin50cos100+i2sin50sin100)
z1×z2=28[cos50cos100+i(sin100cos50+sin50cos100)sin50sin100]
[i2=1]
z1×z2=28[cos50cos100sin50sin100+isin(100+50)]
[sin(A+B)=sinAcosB+cosAsinB]
z1×z2=28[cos(50+100)isin(150)]
[cos(A+B)=cosAcosBsinAsinB]
z1×z2=28(cos150isin150)
Hence,
z1×z2=28(cos150isin150)

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