Hey Sweetie! I'll gladly answer this question for you!
Complex numbers are "binomials" of a sort, and are added, subtracted, and multiplied in a similar way. (Division, which is further down the page, is a bit different.) First, though, you'll probably be asked to demonstrate that you understand the definition of complex numbers.
<span><span>
Solve <span>
3 – 4i = x + yi</span></span>
Finding the answer to this involves nothing more than knowing that two complex numbers can be equal only if their real and imaginary parts are equal. In other words, <span>
3 = x</span>
and <span>
–4 = y</span>
.</span>
To simplify complex-valued expressions, you combine "like" terms and apply the various other methods you learned for working with polynomials.
<span>
Simplify (2 + 3i) + (1 – 6i).</span>
(2 + 3i) + (1 – 6i) = (2 + 1) + (3i – 6i) = 3 + (–3i) = 3 – 3i
<span>
Simplify (5 – 2i) – (–4 – i).</span><span>
(5 – 2i) – (–4 – i)<span>
= (5 – 2i) – 1(–4 – i) = 5 – 2i – 1(–4) – 1(–i)= 5 – 2i + 4 + i= (5 + 4) + (–2i + i)= (9) + (–1i) = 9 – i</span></span>
You may find it helpful to insert the "1" in front of the second set of parentheses (highlighted in red above) so you can better keep track of the "minus" being multiplied through the parentheses.
<span>
Simplify<span>
(2 – i)(3 + 4i).</span></span><span>
(2 – i)(3 + 4i) = (2)(3) + (2)(4i) + (–i)(3) + (–i)(4i)<span>
= 6 + 8i – 3i – 4i2 = 6 + 5i – 4(–1)= 6 + 5i + 4 = <span>
10 + 5i</span>
<span>
That is your answer....
Hope I helped!</span></span></span>
