Solved on Dec 12, 2023

Add or subtract complex numbers. Find the result in standard form. $-7-(4-5i)-(2-4i)$

STEP 1

Assumptions
1. We are dealing with complex numbers.
2. The operation to be performed is subtraction of complex numbers.
3. Standard form of a complex number is $a + bi$ , where $a$ is the real part and $bi$ is the imaginary part.

STEP 2

To subtract complex numbers, subtract the real parts and the imaginary parts separately.
$(a + bi) - (c + di) = (a - c) + (b - d)i$

STEP 3

Write the given expression with clear separation of real and imaginary parts.
$-7 - (4 - 5i) - (2 - 4i)$

STEP 4

Distribute the negative sign across the terms within the parentheses.
$-7 - 4 + 5i - 2 + 4i$

STEP 5

Combine the real parts and the imaginary parts.
Real parts: $-7 - 4 - 2$ Imaginary parts: $5i + 4i$

STEP 6

Calculate the sum of the real parts.
$-7 - 4 - 2 = -13$

STEP 7

Calculate the sum of the imaginary parts.
$5i + 4i = 9i$

STEP 8

Combine the results to write the final answer in standard form.
$-13 + 9i$
The result in standard form is $-13 + 9i$ .

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Add or subtract complex numbers. Find the result in standard form. $-7-(4-5i)-(2-4i)$

STEP 1

Assumptions
1. We are dealing with complex numbers.
2. The operation to be performed is subtraction of complex numbers.
3. Standard form of a complex number is $a + bi$ , where $a$ is the real part and $bi$ is the imaginary part.

STEP 2

To subtract complex numbers, subtract the real parts and the imaginary parts separately.
$(a + bi) - (c + di) = (a - c) + (b - d)i$

STEP 3

Write the given expression with clear separation of real and imaginary parts.
$-7 - (4 - 5i) - (2 - 4i)$

STEP 4

Distribute the negative sign across the terms within the parentheses.
$-7 - 4 + 5i - 2 + 4i$

STEP 5

Combine the real parts and the imaginary parts.
Real parts: $-7 - 4 - 2$ Imaginary parts: $5i + 4i$

STEP 6

Calculate the sum of the real parts.
$-7 - 4 - 2 = -13$

STEP 7

Calculate the sum of the imaginary parts.
$5i + 4i = 9i$

STEP 8

Combine the results to write the final answer in standard form.
$-13 + 9i$
The result in standard form is $-13 + 9i$ .

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Add or subtract complex numbers. Find the result in standard form. −7−(4−5i)−(2−4i)-7-(4-5i)-(2-4i)−7−(4−5i)−(2−4i)

STEP 1

Assumptions1. We are dealing with complex numbers.2. The operation to be performed is subtraction of complex numbers.3. Standard form of a complex number is a+bi a + bi a+bi, where a a a is the real part and bi bi bi is the imaginary part.

STEP 2

To subtract complex numbers, subtract the real parts and the imaginary parts separately.(a+bi)−(c+di)=(a−c)+(b−d)i (a + bi) - (c + di) = (a - c) + (b - d)i (a+bi)−(c+di)=(a−c)+(b−d)i

STEP 3

Write the given expression with clear separation of real and imaginary parts.−7−(4−5i)−(2−4i) -7 - (4 - 5i) - (2 - 4i) −7−(4−5i)−(2−4i)

STEP 4

Distribute the negative sign across the terms within the parentheses.−7−4+5i−2+4i -7 - 4 + 5i - 2 + 4i −7−4+5i−2+4i

STEP 5

Combine the real parts and the imaginary parts.Real parts: −7−4−2 -7 - 4 - 2 −7−4−2 Imaginary parts: 5i+4i 5i + 4i 5i+4i

STEP 6

Calculate the sum of the real parts.−7−4−2=−13 -7 - 4 - 2 = -13 −7−4−2=−13

STEP 7

Calculate the sum of the imaginary parts.5i+4i=9i 5i + 4i = 9i 5i+4i=9i

STEP 8

Combine the results to write the final answer in standard form.−13+9i -13 + 9i −13+9iThe result in standard form is −13+9i -13 + 9i −13+9i.

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Add or subtract complex numbers. Find the result in standard form. $-7-(4-5i)-(2-4i)$

Assumptions
1. We are dealing with complex numbers.
2. The operation to be performed is subtraction of complex numbers.
3. Standard form of a complex number is $a + bi$ , where $a$ is the real part and $bi$ is the imaginary part.

To subtract complex numbers, subtract the real parts and the imaginary parts separately.
$(a + bi) - (c + di) = (a - c) + (b - d)i$

Write the given expression with clear separation of real and imaginary parts.
$-7 - (4 - 5i) - (2 - 4i)$

Distribute the negative sign across the terms within the parentheses.
$-7 - 4 + 5i - 2 + 4i$

Combine the real parts and the imaginary parts.
Real parts: $-7 - 4 - 2$ Imaginary parts: $5i + 4i$

Calculate the sum of the real parts.
$-7 - 4 - 2 = -13$

Calculate the sum of the imaginary parts.
$5i + 4i = 9i$

Combine the results to write the final answer in standard form.
$-13 + 9i$
The result in standard form is $-13 + 9i$ .