write the sum or difference in the standard form a+bi

(2-3i)+(6+5i)

(squareroot5-3i)+(-2+squareroot-9)

(2-3i)+(6+5i)

=2-3i+6+5i
=2+6 -3i+5i
=8+2i
You can do the same procedure for the second part, but change √-9 into 3i before.

To write the sum or difference in standard form, we simplify the expression by combining the real and imaginary parts.

1. (2-3i) + (6+5i):
By adding the real parts and the imaginary parts, we get:
(2 + 6) + (-3 + 5)i
8 + 2i

Therefore, (2-3i) + (6+5i) in standard form is 8 + 2i.

2. (√5 - 3i) + (-2 + √-9):
Simplify the expression by combining the real and imaginary parts:
(√5 - 2) + (-3 + √-9)i

To simplify further, let's express √-9 in terms of i:
√-9 = √(-1 * 9) = √(-1) * √9 = i * 3i = 3i^2
Since i^2 = -1, the expression becomes:
(√5 - 2) + (-3 + 3i^2)i

Now, multiply i^2 by the coefficient -3:
(√5 - 2) + (-3 - 3i)i
(√5 - 2) + (-3i - 3i^2)
(√5 - 2) + (-3i + 3)
(√5 - 2) - 3i + 3

Combine the real and imaginary parts:
(√5 - 2 + 3) - 3i
(√5 + 1) - 3i

Therefore, (√5 - 3i) + (-2 + √-9) in standard form is (√5 + 1) - 3i.

To write the sum or difference in the standard form a + bi, you need to combine the real parts (a) and the imaginary parts (b) separately.

Let's solve the first expression:
(2 - 3i) + (6 + 5i)

To combine the real parts, you add 2 and 6:
2 + 6 = 8

To combine the imaginary parts, you add -3i and +5i:
-3i + 5i = 2i

Therefore, the sum (2 - 3i) + (6 + 5i) is in the standard form a + bi as follows:
8 + 2i

Now, let's solve the second expression:
(sqrt(5) - 3i) + (-2 + sqrt(-9))

To combine the real parts, you add sqrt(5) and -2:
sqrt(5) - 2

To combine the imaginary parts, you add -3i and sqrt(-9).
Since sqrt(-9) equals 3i (the square root of -1 is 'i'), you have:
-3i + 3i = 0

Therefore, the sum (sqrt(5) - 3i) + (-2 + sqrt(-9)) is in the standard form a + bi as follows:
sqrt(5) - 2 + 0i, which can be simplified to:
sqrt(5) - 2