QuestionFind the sum and express it as $a + bi$ : $(2 - 5i) + \left(-5 - \frac{4}{3}i\right)$ .

Studdy Solution

STEP 1

Assumptions1. We are dealing with complex numbers, which are in the form $a + bi$ , where $a$ is the real part and $b$ is the imaginary part. . We are asked to add two complex numbers $(-5i)$ and $\left(-5-\frac{4}{3}i\right)$ .

STEP 2

To add two complex numbers, we add 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.
$(2 -5i) + \left(-5 - \frac{}{3}i\right) = (2 -5) + (-5 - \frac{}{3})i$

STEP 4

Perform the addition for the real parts and the imaginary parts separately.
$(2 -) + (- - \frac{4}{3})i = -3 - \frac{19}{3}i$

STEP 5

The result is a complex number in the form $a + bi$ , where $a = -3$ and $b = -\frac{19}{3}$ .
So, the sum of the two complex numbers $(2-5i)$ and $\left(-5-\frac{4}{3}i\right)$ is $-3 - \frac{19}{3}i$ .

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QuestionFind the sum and express it as $a + bi$ : $(2 - 5i) + \left(-5 - \frac{4}{3}i\right)$ .

Studdy Solution

STEP 1

Assumptions1. We are dealing with complex numbers, which are in the form $a + bi$ , where $a$ is the real part and $b$ is the imaginary part. . We are asked to add two complex numbers $(-5i)$ and $\left(-5-\frac{4}{3}i\right)$ .

STEP 2

To add two complex numbers, we add 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.
$(2 -5i) + \left(-5 - \frac{}{3}i\right) = (2 -5) + (-5 - \frac{}{3})i$

STEP 4

Perform the addition for the real parts and the imaginary parts separately.
$(2 -) + (- - \frac{4}{3})i = -3 - \frac{19}{3}i$

STEP 5

The result is a complex number in the form $a + bi$ , where $a = -3$ and $b = -\frac{19}{3}$ .
So, the sum of the two complex numbers $(2-5i)$ and $\left(-5-\frac{4}{3}i\right)$ is $-3 - \frac{19}{3}i$ .

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QuestionFind the sum and express it as a+bia + bia+bi: (2−5i)+(−5−43i)(2 - 5i) + \left(-5 - \frac{4}{3}i\right)(2−5i)+(−5−34​i).

Studdy Solution

STEP 1

Assumptions1. We are dealing with complex numbers, which are in the form a+bia + bia+bi, where aaa is the real part and bbb is the imaginary part. . We are asked to add two complex numbers (−5i)(-5i)(−5i) and (−5−43i)\left(-5-\frac{4}{3}i\right)(−5−34​i).

STEP 2

To add two complex numbers, we add 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.(2−5i)+(−5−3i)=(2−5)+(−5−3)i (2 -5i) + \left(-5 - \frac{}{3}i\right) = (2 -5) + (-5 - \frac{}{3})i (2−5i)+(−5−3​i)=(2−5)+(−5−3​)i

STEP 4

Perform the addition for the real parts and the imaginary parts separately.(2−)+(−−43)i=−3−193i (2 -) + (- - \frac{4}{3})i = -3 - \frac{19}{3}i (2−)+(−−34​)i=−3−319​i

STEP 5

The result is a complex number in the form a+bia + bia+bi, where a=−3a = -3a=−3 and b=−193b = -\frac{19}{3}b=−319​.So, the sum of the two complex numbers (2−5i)(2-5i)(2−5i) and (−5−43i)\left(-5-\frac{4}{3}i\right)(−5−34​i) is −3−193i-3 - \frac{19}{3}i−3−319​i.

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QuestionFind the sum and express it as $a + bi$ : $(2 - 5i) + \left(-5 - \frac{4}{3}i\right)$ .

Assumptions1. We are dealing with complex numbers, which are in the form $a + bi$ , where $a$ is the real part and $b$ is the imaginary part. . We are asked to add two complex numbers $(-5i)$ and $\left(-5-\frac{4}{3}i\right)$ .

To add two complex numbers, we add 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.
$(2 -5i) + \left(-5 - \frac{}{3}i\right) = (2 -5) + (-5 - \frac{}{3})i$

Perform the addition for the real parts and the imaginary parts separately.
$(2 -) + (- - \frac{4}{3})i = -3 - \frac{19}{3}i$

The result is a complex number in the form $a + bi$ , where $a = -3$ and $b = -\frac{19}{3}$ .
So, the sum of the two complex numbers $(2-5i)$ and $\left(-5-\frac{4}{3}i\right)$ is $-3 - \frac{19}{3}i$ .