Linear combination of complex

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

a) 4z1+6z2
b) z1*z2

Correct answer:

x =  44
y = 26+2i

Step-by-step explanation:

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​⋅ 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

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