Simplify each of the following, giving your answer in the form a+bi, where a, b, e, z:

Question

A). (3-4i)-(-6+5i)
B). (2-3i)^2/1+2i

Answer 1

A). (3-4i)-(-6+5i)
To simplify this, we can distribute the negative sign when subtracting:

(3-4i)+6-5i

Combine like terms:

9 - 9i

So the simplified form is 9 - 9i.

B). (2-3i)^2/1+2i
To simplify this, we can start by squaring the numerator:

(2-3i)(2-3i)

Using FOIL method:

4 - 6i - 6i + 9i^2

Simplify the middle terms and replace i^2 with -1:

4 - 12i + 9(-1)

Combine like terms:

4 - 12i - 9

-5 - 12i

Now let's simplify the denominator:

1+2i

To rationalize this, we multiply the numerator and denominator by the conjugate of 1+2i, which is 1-2i:

(-5-12i)(1-2i)/(1+2i)(1-2i)

Using FOIL method:

(-5+10i-12i+24i^2)/(1-2i+2i-4i^2)

Simplify the middle terms and replace i^2 with -1:

(-5-2i+24(-1))/(1-4(-1))

Simplify further:

(-5-2i-24)/(1+4)

Combine like terms:

(-29-2i)/5

So the simplified form is (-29-2i)/5.