Question

Whats the product of (3-4i)(1-i) =

Answer 1

`(3-4i)(1-i)= -7i-1`

Explanation:

To find the product of two complex numbers, you can use the distributive property and the fact that "i² = -1."

We have,

`\rightarrow (3-4i)(1-i)\\\\\\\Longrightarrow (3)(1)+(3)(-i)+(-4i)(1)+(-4i)(-i)\\\\\\\Longrightarrow 3-3i-4i+4i^2\\\\\\\Longrightarrow 4i^2+(-3i-4i)+3\\\\\\\Longrightarrow 4i^2-7i+3`

Now, since "i² = -1," we can substitute it into the expression and simplify:

`\Longrightarrow 4i^2-7i+3\\\\\\\Longrightarrow 4(-1)-7i+3\\\\\\\Longrightarrow -4-7i+3\\\\\\\Longrightarrow -7i+(3-4)\\\\\\\therefore -7i-1`

Thus, the problem is solved.

Answer 2

Hello!

Answer:

`\Large \boxed{\sf -1 - 7i}`

Explanation:

`\sf (3-4i)(1-i) \\\\= (3x1) + (3 x -i) + (-4i x 1) + ( -4i x -i) \\\\= 3 - 3i - 4i -4 \\\\\boxed{\sf = -1 - 7i}`