Question

Poducts  z1 and z2 as a z1=5+3i and z2=4-2i, write the following in the form a+bi

Answer 1

Given

z1=5+3i 

z2​ =4−2i 

 

x=4⋅ z1+6⋅ z2

​

  

x=4⋅ (5+3i)+6⋅ (4−2i) 

x=20+12i+24−12i 

x=(20+24)+(12−12)i 

x=44

y=z1⋅ z 2

​

  

y=(5+3i)⋅ (4−2i) 

=5⋅ 4+5⋅ (−2i)+3i⋅ z 1

​=5+3i 

z 2

=4−2i 

 

x=4⋅ z 1+6⋅ z 2

​x=4⋅ (5+3i)+6⋅ (4−2i) 

x=20+12i+24−12i 

x=(20+24)+(12−12)i 

x=44

y=z 1⋅ z2

​

  

y=(5+3i)⋅ (4−2i) 

5⋅ 4+5⋅ (−2i)+3i⋅ 4+3i⋅ (−2i) 

y=20−10i+12i−6i²

  

y=20−10i+12i+6 

y=20+6+i(−10+12) 

y=26+2i

⋅ (−2i) 

y=20−10i+12i−6i²

  

y=20−10i+12i+6 

y=20+6+i(−10+12) 

y=26+2i