Math / Algebra

QuestionSubtract. $(14+i)-(-1+4 i)$

Studdy Solution

STEP 1

1. We are dealing with complex numbers.
2. The subtraction of complex numbers involves subtracting both the real and imaginary parts separately.

STEP 2

1. Identify the real and imaginary components of each complex number.
2. Subtract the real parts.
3. Subtract the imaginary parts.
4. Combine the results to form the final complex number.

STEP 3

Identify the real and imaginary parts of each complex number:
- For $14 + i$ , the real part is $14$ and the imaginary part is $i$ . - For $-1 + 4i$ , the real part is $-1$ and the imaginary part is $4i$ .

STEP 4

Subtract the real parts:
$14 - (-1) = 14 + 1 = 15$

STEP 5

Subtract the imaginary parts:
$i - 4i = 1i - 4i = -3i$

STEP 6

Combine the results to form the final complex number:
$15 - 3i$
The result of the subtraction is:
$\boxed{15 - 3i}$

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QuestionSubtract. $(14+i)-(-1+4 i)$

Studdy Solution

STEP 1

1. We are dealing with complex numbers.
2. The subtraction of complex numbers involves subtracting both the real and imaginary parts separately.

STEP 2

1. Identify the real and imaginary components of each complex number.
2. Subtract the real parts.
3. Subtract the imaginary parts.
4. Combine the results to form the final complex number.

STEP 3

Identify the real and imaginary parts of each complex number:
- For $14 + i$ , the real part is $14$ and the imaginary part is $i$ . - For $-1 + 4i$ , the real part is $-1$ and the imaginary part is $4i$ .

STEP 4

Subtract the real parts:
$14 - (-1) = 14 + 1 = 15$

STEP 5

Subtract the imaginary parts:
$i - 4i = 1i - 4i = -3i$

STEP 6

Combine the results to form the final complex number:
$15 - 3i$
The result of the subtraction is:
$\boxed{15 - 3i}$

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QuestionSubtract. (14+i)−(−1+4i)(14+i)-(-1+4 i)(14+i)−(−1+4i)

Studdy Solution

STEP 1

1. We are dealing with complex numbers.2. The subtraction of complex numbers involves subtracting both the real and imaginary parts separately.

STEP 2

1. Identify the real and imaginary components of each complex number.2. Subtract the real parts.3. Subtract the imaginary parts.4. Combine the results to form the final complex number.

STEP 3

Identify the real and imaginary parts of each complex number:- For 14+i 14 + i 14+i, the real part is 14 14 14 and the imaginary part is i i i. - For −1+4i -1 + 4i −1+4i, the real part is −1 -1 −1 and the imaginary part is 4i 4i 4i.

STEP 4

Subtract the real parts:14−(−1)=14+1=15 14 - (-1) = 14 + 1 = 15 14−(−1)=14+1=15

STEP 5

Subtract the imaginary parts:i−4i=1i−4i=−3i i - 4i = 1i - 4i = -3i i−4i=1i−4i=−3i

STEP 6

Combine the results to form the final complex number:15−3i 15 - 3i 15−3iThe result of the subtraction is:15−3i \boxed{15 - 3i} 15−3i​

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QuestionSubtract. $(14+i)-(-1+4 i)$

1. We are dealing with complex numbers.
2. The subtraction of complex numbers involves subtracting both the real and imaginary parts separately.

1. Identify the real and imaginary components of each complex number.
2. Subtract the real parts.
3. Subtract the imaginary parts.
4. Combine the results to form the final complex number.

Identify the real and imaginary parts of each complex number:
- For $14 + i$ , the real part is $14$ and the imaginary part is $i$ . - For $-1 + 4i$ , the real part is $-1$ and the imaginary part is $4i$ .

Subtract the real parts:
$14 - (-1) = 14 + 1 = 15$

Subtract the imaginary parts:
$i - 4i = 1i - 4i = -3i$

Combine the results to form the final complex number:
$15 - 3i$
The result of the subtraction is:
$\boxed{15 - 3i}$