First, let's simplify each part of the expression separately:
(7+2i)^2 = (7+2i)(7+2i)Expanding using FOIL (First, Outer, Inner, Last):= 77 + 72i + 2i7 + 2i2i= 49 + 14i + 14i + 4i^2= 49 + 28i + 4(-1)= 49 + 28i - 4= 45 + 28i
Next, let's simplify (6+8i)(6-8i):= 66 + 6(-8i) + 8i6 + 8i*(-8i)= 36 - 48i + 48i - 64i^2= 36 - 64(-1)= 36 + 64= 100
Now, let's multiply the two simplified expressions:(45 + 28i)*100= 4500 + 2800i
Therefore, (7+2i)^2 (6+8i)(6-8i) = 4500 + 2800i.
First, let's simplify each part of the expression separately:
(7+2i)^2 = (7+2i)(7+2i)
Expanding using FOIL (First, Outer, Inner, Last):
= 77 + 72i + 2i7 + 2i2i
= 49 + 14i + 14i + 4i^2
= 49 + 28i + 4(-1)
= 49 + 28i - 4
= 45 + 28i
Next, let's simplify (6+8i)(6-8i):
= 66 + 6(-8i) + 8i6 + 8i*(-8i)
= 36 - 48i + 48i - 64i^2
= 36 - 64(-1)
= 36 + 64
= 100
Now, let's multiply the two simplified expressions:
(45 + 28i)*100
= 4500 + 2800i
Therefore, (7+2i)^2 (6+8i)(6-8i) = 4500 + 2800i.