Question

If (a = -5x) and (b = -5x - 2i), then find the value of (a ast b) in fully simplified form.

a) (25x² + 10ix)
b) (25x² - 10ix)
c) (-25x² - 10ix)
d) (-25x² + 10ix)

Answer 1

The product of complex numbers a and b, given as a = -5x and b = -5x - 2i, is calculated to be (25x² + 10ix), which is answer choice a).

Step-by-step explanation:

The question concerns the multiplication of two complex numbers, a and b, where a = -5x and b = -5x - 2i. To find the product (a * b), we use the formula for multiplying complex numbers: (a + ib)(a - ib) = a² + b².

Substituting in the given values:

• a = -5x
• b = -5x - 2i

The product (a * b) is:

1. (-5x) * (-5x) = 25x²
2. (-5x) * (-2i) = 10ix

So the fully simplified form of (a * b) is (25x² + 10ix), which corresponds to answer choice a).