Questions: Practice Problems 1. Write the sum or difference in the standard form a+bi without using a calculator. a. (2-3 i)+(6+5 i) b. (2+i)-(9 i-3)

Solution Steps

To solve these problems, we need to perform basic arithmetic operations on complex numbers. For each part, we will add or subtract the real parts and the imaginary parts separately.

1. Add the real parts: \(2 + 6\)
2. Add the imaginary parts: \(-3i + 5i\)

1. Subtract the real parts: \(2 - (-3)\)
2. Subtract the imaginary parts: \(i - 9i\)

To find the sum of the real parts in part (a), we calculate: \[ 2 + 6 = 8 \]

To find the sum of the imaginary parts in part (a), we calculate: \[ -3i + 5i = 2i \]

Combining the real and imaginary parts, we get: \[ (2 - 3i) + (6 + 5i) = 8 + 2i \]

To find the difference of the real parts in part (b), we calculate: \[ 2 - (-3) = 2 + 3 = 5 \]

To find the difference of the imaginary parts in part (b), we calculate: \[ i - 9i = 1i - 9i = -8i \]

Combining the real and imaginary parts, we get: \[ (2 + i) - (9i - 3) = 5 - 8i \]

Final Answer