Question

multiply (4t²+6p²-12p²t²q) by-½pqt​

Answer 1

Complex multiplication is a more difficult operation to understand from either an algebraic or a geometric point of view. Let’s do it algebraically first, and let’s take specific complex numbers to multiply, say 3 + 2i and 1 + 4i. Each has two terms, so when we multiply them, we’ll get four terms:

(3 + 2i)(1 + 4i) = 3 + 12i + 2i + 8i2.

Now the 12i + 2i simplifies to 14i, of course. What about the 8i2? Remember we introduced i as an abbreviation for √–1, the square root of –1. In other words, i is something whose square is –1. Thus, 8i2 equals –8. Therefore, the product (3 + 2i)(1 + 4i) equals –5 + 14i.

If you generalize this example, you’ll get the general rule for multiplication

(x+yi)(u+vi) = (xu=yv)+(xv+yu)i

Remember that (xu – yv), the real part of the product, is the product of the real parts minus the product of the imaginary parts, but (xv + yu), the imaginary part of the product, is the sum of the two products of one real part and the other imaginary part.

Let’s look at some special cases of multiplication.