Question

If a = 1 + 4i and b = 2, then find the value of a^2 * b in fully simplified form.

a) 10 + 9i
b) -14 + 10i
c) 18 + 2i
d) -6 - 8i

Answer 1

The value of a^2 * b, where a = 1 + 4i and b = 2, is calculated by first squaring the complex number a to get -15 + 8i and then multiplying this result by b to get the fully simplified value of -30 + 16i.

Step-by-step explanation:

To find the value of a2 * b, where a = 1 + 4i and b = 2, we first calculate a2. We do this by squaring the complex number a:

(1 + 4i)2 = (1 + 4i)(1 + 4i) = 1 + 4i + 4i + 16i2

Since i2 = -1, we can simplify it further:

1 + 8i - 16 = -15 + 8i

Now we can calculate a2 * b by multiplying this result by b, which is 2:

(-15 + 8i) * 2 = -30 + 16i

So the fully simplified value of a2 * b is -30 + 16i.