(7+3i)(-7+5i)(-8-4i)

2 min read Jun 16, 2024
(7+3i)(-7+5i)(-8-4i)

Multiplying Complex Numbers: (7+3i)(-7+5i)(-8-4i)

This article will guide you through multiplying three complex numbers: (7+3i)(-7+5i)(-8-4i). We will break down the process step by step to make it easier to follow.

Step 1: Multiply the first two complex numbers

We start by multiplying the first two complex numbers: (7+3i)(-7+5i).

To do this, we use the distributive property (or FOIL method):

(7+3i)(-7+5i) = (7)(-7) + (7)(5i) + (3i)(-7) + (3i)(5i)

Simplifying:

= -49 + 35i - 21i + 15i²

Remember that i² = -1. Substituting this:

= -49 + 35i - 21i - 15 
= -64 + 14i

Step 2: Multiply the result by the third complex number

Now we have (-64 + 14i) and we need to multiply it by (-8-4i):

(-64 + 14i)(-8-4i) = (-64)(-8) + (-64)(-4i) + (14i)(-8) + (14i)(-4i)

Simplifying:

= 512 + 256i - 112i - 56i²

Again, substitute i² = -1:

= 512 + 256i - 112i + 56 
= 568 + 144i

Final Result

Therefore, the product of (7+3i)(-7+5i)(-8-4i) is 568 + 144i.

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