Math

QuestionAdd and simplify: (1711i)+(20+3i)(17-11 i)+(20+3 i); Subtract and simplify: (1711i)(20+3i)(17-11 i)-(20+3 i).

Studdy Solution

STEP 1

Assumptions1. We are dealing with complex numbers. In a complex number, the real part is the number without the "i" and the imaginary part is the number with the "i".. We are asked to perform two operations addition and subtraction.

STEP 2

First, let's perform the addition operation. We can add complex numbers by adding the real parts together and the imaginary parts together.
sum=(Realpartoffirstnumber+Realpartofsecondnumber)+(Imaginarypartoffirstnumber+Imaginarypartofsecondnumber)i\text{sum} = (Real\, part\, of\, first\, number + Real\, part\, of\, second\, number) + (Imaginary\, part\, of\, first\, number + Imaginary\, part\, of\, second\, number)i

STEP 3

Now, plug in the given values for the real and imaginary parts of the two complex numbers.
sum=(17+20)+(11+3)i\text{sum} = (17 +20) + (-11 +3)i

STEP 4

Perform the addition operation.
sum=378i\text{sum} =37 -8i

STEP 5

Next, let's perform the subtraction operation. We can subtract complex numbers by subtracting the real parts and the imaginary parts separately.
difference=(RealpartoffirstnumberRealpartofsecondnumber)+(ImaginarypartoffirstnumberImaginarypartofsecondnumber)i\text{difference} = (Real\, part\, of\, first\, number - Real\, part\, of\, second\, number) + (Imaginary\, part\, of\, first\, number - Imaginary\, part\, of\, second\, number)i

STEP 6

Now, plug in the given values for the real and imaginary parts of the two complex numbers.
difference=(1720)+(113)i\text{difference} = (17 -20) + (-11 -3)i

STEP 7

Perform the subtraction operation.
difference=314i\text{difference} = -3 -14iSo, the sum of the two complex numbers is 37i37 -i and the difference is 314i-3 -14i.

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