Question

If a = 5 + 4i and b = -3x, then find
the value of the a²b in fully simplified
form.

Answer 1

-27x-120xi

Explanation:

(5+4i)^2(3x)
split it into (5+4i)(5+4i)

(25+20i+20i+16i^2)(3x)

(25+40i+16i^2)(3x)

Now, let's find a²b:

a²b = (25 + 40i + 16i²)(-3x)

Since i² is equal to -1, we can simplify further:

a²b = (25 + 40i - 16)(-3x)

a²b = (9 + 40i)(-3x)
Now, multiply the real and imaginary parts separately:

Real part:

9 * (-3x) = -27x

Imaginary part:

40i * (-3x) = -120xi
so a^2b = -27x-120xi