QuestionFind the sum of the complex numbers $(7+3i) + (-8+9i)$ . What is the result? A) $-1+12i$ B) $-1-6i$ C) $15+12i$ D) $15-6i$

Studdy Solution

STEP 1

Assumptions1. We are dealing with complex numbers, where $i=\sqrt{-1}$ . . We are asked to find the sum of two complex numbers $(7+3 i)$ and $(-8+9 i)$ .

STEP 2

The sum of two complex numbers is found by adding the real parts together and the imaginary parts together. $(a + bi) + (c + di) = (a + c) + (b + d)i$

STEP 3

Now, plug in the given values for the real and imaginary parts of the two complex numbers into the formula.
$(7 +3i) + (-8 +9i) = (7 -8) + (3 +9)i$

STEP 4

Calculate the real part of the sum.
$7 -8 = -1$

STEP 5

Calculate the imaginary part of the sum.
$3 +9 =12$

STEP 6

Combine the real and imaginary parts to form the sum of the two complex numbers.
$-1 +12i$ So, the sum of $(+3 i)$ and $(-8+9 i)$ is $-1+12 i$ .

Was this helpful?

QuestionFind the sum of the complex numbers $(7+3i) + (-8+9i)$ . What is the result? A) $-1+12i$ B) $-1-6i$ C) $15+12i$ D) $15-6i$

Studdy Solution

STEP 1

Assumptions1. We are dealing with complex numbers, where $i=\sqrt{-1}$ . . We are asked to find the sum of two complex numbers $(7+3 i)$ and $(-8+9 i)$ .

STEP 2

The sum of two complex numbers is found by adding the real parts together and the imaginary parts together. $(a + bi) + (c + di) = (a + c) + (b + d)i$

STEP 3

Now, plug in the given values for the real and imaginary parts of the two complex numbers into the formula.
$(7 +3i) + (-8 +9i) = (7 -8) + (3 +9)i$

STEP 4

Calculate the real part of the sum.
$7 -8 = -1$

STEP 5

Calculate the imaginary part of the sum.
$3 +9 =12$

STEP 6

Combine the real and imaginary parts to form the sum of the two complex numbers.
$-1 +12i$ So, the sum of $(+3 i)$ and $(-8+9 i)$ is $-1+12 i$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the sum of the complex numbers (7+3i)+(−8+9i)(7+3i) + (-8+9i)(7+3i)+(−8+9i). What is the result? A) −1+12i-1+12i−1+12i B) −1−6i-1-6i−1−6i C) 15+12i15+12i15+12i D) 15−6i15-6i15−6i

Studdy Solution

STEP 1

Assumptions1. We are dealing with complex numbers, where i=−1i=\sqrt{-1}i=−1​. . We are asked to find the sum of two complex numbers (7+3i)(7+3 i)(7+3i) and (−8+9i)(-8+9 i)(−8+9i).

STEP 2

The sum of two complex numbers is found by adding the real parts together and the imaginary parts together.(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

Now, plug in the given values for the real and imaginary parts of the two complex numbers into the formula.(7+3i)+(−8+9i)=(7−8)+(3+9)i (7 +3i) + (-8 +9i) = (7 -8) + (3 +9)i (7+3i)+(−8+9i)=(7−8)+(3+9)i

STEP 4

Calculate the real part of the sum.7−8=−17 -8 = -1 7−8=−1

STEP 5

Calculate the imaginary part of the sum.3+9=123 +9 =12 3+9=12

STEP 6

Combine the real and imaginary parts to form the sum of the two complex numbers.−1+12i -1 +12i −1+12iSo, the sum of (+3i)(+3 i)(+3i) and (−8+9i)(-8+9 i)(−8+9i) is −1+12i-1+12 i−1+12i.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the sum of the complex numbers $(7+3i) + (-8+9i)$ . What is the result? A) $-1+12i$ B) $-1-6i$ C) $15+12i$ D) $15-6i$

Assumptions1. We are dealing with complex numbers, where $i=\sqrt{-1}$ . . We are asked to find the sum of two complex numbers $(7+3 i)$ and $(-8+9 i)$ .

The sum of two complex numbers is found by adding the real parts together and the imaginary parts together. $(a + bi) + (c + di) = (a + c) + (b + d)i$

Now, plug in the given values for the real and imaginary parts of the two complex numbers into the formula.
$(7 +3i) + (-8 +9i) = (7 -8) + (3 +9)i$

Calculate the real part of the sum.
$7 -8 = -1$

Calculate the imaginary part of the sum.
$3 +9 =12$

Combine the real and imaginary parts to form the sum of the two complex numbers.
$-1 +12i$ So, the sum of $(+3 i)$ and $(-8+9 i)$ is $-1+12 i$ .