Can anyone simplify this (3+4i)(2-i) in the form a+bi.?

Question

Can anyone simplify this (3+4i)(2-i) in the form a+bi. a and b are real numbers. I just can’t do it. Its so frustrating.

Answer 1

Just multiply the stuff together, FOIL-style.
(3+4i)(2-i)
6 -3i +8i -4i^2
6 + 5i -4*(-1)
6+5i +4
10 + 5i

There, not so hard, is it? :-)

Answer 2

Multiplying complex numbers is just the same as multiplying an expression.
Just like the way you do:
(x+3)(y-4)
You use the FOIL method.
(3 +4i) (2- i)
Multiply the FIRST TERM:
(3)(2)
Multiply the OUTER TERM:
(3)(-i)
Multiply the INNER TERM:
(4i)(2)
Multiply the LAST TERM:
(4i)(-i)
Then adding all these terms, gives:
6 - 3i +8i - 4i^2
combine similar terms:
6 + 5i -4i^2
For the imaginary number i, we know that:
i=sq.root(-1)
so, i^2 means:
sq.root(-1)^2
since the square root and the squared cancels each others effect:
i^2= -1
substituting this to the equation gives:
6 + 5i -4(-1)
6 +5i +4
combining similar terms, gives the final answer:
10 + 5i

Answer 3

Note that i² = - 1
(3 + 4i).(2 - i) = 6 - 3i + 8i - 4i² = 6 + 5i + 4 = 10 + 5i

Answer 4

(3 + 4i)(2 - i)
This works the same as multiplying two binomials such as 4x+1 and 5x-8
(4x + 1)(5x - 8) = (4x)(5x) + (4x)(-8) + (1)(5x) + (1)(-8)
= 20x^2 - 32x + 5x - 8
=20x^2 - 27x - 8

The only difference is that with i, because of the definition of i, you replace i with -1 and continue to simplify.

So, as an example:
(7 + 3i)(2 - 4i) = (7)(2) + (7)(-4i) + (3i)(2) + (3i)(-4i)
= 14 - 28i + 6i -12i^2
= 14 - 22i -12(-1), since by definition i^2 = -1
= 14 - 22i + 12
= 26 - 22i

As a math teacher, I have a difficult time just giving an answer. I hope this helps you understand so you can do any other problem like this.

Answer 5

(3+4i)(2-i)

use the foil.

=6+5i-4i^2
remember that i^2=-1
=6+5i-4(-1)
=6+5i+4
=10+5i answer

Answer 6

(3 + 4i)(2 - i)

First, FOIL it out.

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

Remember though that i^2 = -1.

6 - 3i + 8i - 4(-1)

Simplify and group like terms.

6 + 5i + 5

11 + 5i

Answer 7

Factor it out..or multiply..whatever the word is...i'll say expand

6+8i-3i-4i^2
i = square root of -1
so i^2 = -1....
square root of 2 * square root of 2 = 2
so square root of -1 * square root of -1 = -1
6+5i-4(-1)
6+4+5i
10+5i

Answer 8

10+5i