Write the expression as a complex number in standard form

Question

Write the expression as a complex number in standard form

7+3i/4-i 

Answer 1

So the first step in approaching this problem is realizing that standard form means no i in the denominator. As you may have learned in class, an expression with an i in it can be rid of that i if you multiply by its conjugate. For example, (1−8i) (1+8i) = 1+8i − 8i − 64i^2 =1+64 = 65. As you can see, there are no i's in our answer. So the next thing to do for your problem is to multiply your given expression by the conjugate of the denominator. But be careful; we don't want to just randomly multiply by some number, the rules of Algebra don't allow for that! So to sneak in our conjugate and get rid of that i in the denominator, multiply your entire expression by the conjugate of the denominator/conjugate of the denominator. Because remember, any number divided by itself is 1 so we're technically just multiplying the original equation by one. Then do all of the multiplying out (the tedious part) and make sure you don't drop any negatives! That's how you'll solve this problem. Let me know if you need more help!

Answer 2

7+3i/4-i 

I assume that you mean (7+3i)/(4-i) Otherwise the problem is too easy!!

Whenever you have this kind of expression with complex numbers, clear the imaginary part 

from the denominator by multiplying top and bottom by the conjugate---as follows:

(7+3i)/(4-i) * (4 + i)/(4 + i) =

(28 + 19i - 3)/(16 + 1)

continue to simplify by combining the real parts