Find the product (2+i)(3+4i). Give your answer in the usual a+bi form.?

Answer 1

You can do this by hand the same way you multiply polynomials - use the FOIL method.

(2 + i) (3 + 4i) = (2*3) + (2 * 4i) + (3 * i) + (4i * i)

= 6 + 8i + 3i - 4

= (2 + 11i)

You could also convert to polar coordinates:

2^2 + 1^2 = R1^2
5 = R1^2
sqrt(5) = R

tan (Q1) = 1/2
Q1 = 27.5 deg

3^2 + 4^2 = R2^2
25 = R2^2
5 = R2

tan (Q2) = 5/4
Q2 = 51.4 deg

5* sqrt(5) = R3
Q3 = 27.5 deg + 51.4 deg
Q3 = 78.9 deg

Convert back to a complex number:

5*sqrt(5) * cos(78.9) = 2.07
5 * sqrt*5) * sin(78.9) = 10.95
These are rounded off (especially the angle), so the answer is: 2 + 11i, the same as the foil method.

The second method seems complicated, but it does wind up being the easier method for calculating impedances in electronic circuits, which usually involve more than just two complex numbers.

Answer 2

First: use the foiling method ...

(2)(3) + 2(4i) + i(3) + i(4i)

Sec: combine the terms ...

6 + 8i + 3i + 4i^2

6 + 11i + 4i^2

Third: i^2 is -1 ...replace -1 with i^2 in the expression ..

6 + 11i + 4(-1)

6 + 11i - 4

6 - 4 + 11i

2 + 11i

Answer 3

(2+i)(3+4i) =
6 + 3i + 8i + 4i^2 =

6 + 11 i -4 =

2 + 11i

Answer 4

(2 + I)(3 + 4i) =

6 + 3i + 8i + 4i²=

6 11i + 4i² =

6 + 11i + 4(- 1) =

6 + 11i + (- 4) =

6 + 11i - 4 =

2 + 11i

The answer is 2 + 11i

- - - - - - - - -s-

Answer 5

you should "foil" to get the product.

(2 + i )( 3+ 4i) = 6 + 8i + 3i +4i^2
6 + 11i - 4
2 + 11i

Answer 6

there are 2 achievable superb solutions via unviable illustration. if (5+3i)/(2+4i) : we ought to get the i out of the denominator like this: (5+3i)(2-4i)/(2+4i)(2-4i), simplified: (a million.a million- 0.7i). or this: 5+a million.5i+4i artwork this form: 5.5i+5. in basic terms one is actual reckoning on the acual difficulty. desire i helped

Answer 7

(2+i)(3+4i)= 6+8i+3i+(4i x i)
i multiplied by i gives you an answer of -1
6+8i+3i-4
combine like terms
2+11i
is your answer

Answer 8

we can get real numbers by multiplying two real numbers and then also by multplying 2 imaginary numbers.
Also imaginary numbers are obtained by multiplying the imaginary numbers with the real numbers
so (2+i)(3+4i) = 6+(-4) +i(8+3)
= 2 + i11