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Math  /  Algebra

QuestionFind the sum of the pair of complex numbers. Then graph both complex numbers and their resultant. 5−6i,−2+4i5-6 i,-2+4 i
The sum is □\square (Type your answer in the form a+bi\mathrm{a}+\mathrm{bi}.)

Studdy Solution

STEP 1

1. Complex numbers are of the form a+bi a + bi , where a a is the real part and b b is the imaginary part.
2. To find the sum of complex numbers, we add their real parts and their imaginary parts separately.

STEP 2

1. Identify the real and imaginary parts of each complex number.
2. Add the real parts together.
3. Add the imaginary parts together.
4. Write the sum in the form a+bi a + bi .
5. Graph the complex numbers and their resultant.

STEP 3

Identify the real and imaginary parts of each complex number. For the complex number 5−6i 5 - 6i , the real part is 5 5 and the imaginary part is −6-6. For the complex number −2+4i-2 + 4i, the real part is −2-2 and the imaginary part is 44.

STEP 4

Add the real parts of the complex numbers:
5+(−2)=3 5 + (-2) = 3

STEP 5

Add the imaginary parts of the complex numbers:
−6+4=−2 -6 + 4 = -2

STEP 6

Combine the results from Step 2 and Step 3 to write the sum in the form a+bi a + bi :
3−2i 3 - 2i

STEP 7

Graph the complex numbers and their resultant: - Plot the point (5,−6) (5, -6) for the complex number 5−6i 5 - 6i . - Plot the point (−2,4) (-2, 4) for the complex number −2+4i-2 + 4i. - Plot the point (3,−2) (3, -2) for the resultant complex number 3−2i 3 - 2i . - Draw vectors from the origin to each of these points to represent the complex numbers.
The sum of the pair of complex numbers is:
3−2i \boxed{3 - 2i}

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