Express in the form a+bi where a&b are real numbers.

Express in the form a+bi where a&b are real numbers.

1. (2+5i)-(3-4i): 2 + 5i - 3 +4i = -1 +9i

2. (4-3i)(2+i): 4*2 +4i -6i -3i*i = 8 -2i -3(-1) = 11 - 2i       | i*i = -1 !

3. i (3-2i)^2: i(3*3-2*3*2i + 4i*i) = i(9-12i-4) = i(5-12i) = 5i -12i*i = 5i + 12 = 12 + 5i

4. i^52: (i*i)^26 = (-1)^26 = 1

5. 1+5i / 1-2i = $$\small{\text{
$
\frac{1+5i} {1-2i} = \frac{(1+5i)(1+2i)} {(1-2i)(1+2i)} = \frac{1*1+7i+10i*i}{1-4i*i}=\frac{1+7i-10}{1+4} =\frac{-9+7i}{5} =-\frac{9}{5}+\frac{7}{5}i
$
}}$$

6. 7+3i / 4i = $$\small{\text{
$
\frac{7+3i} {4i} = \frac{(7+3i)(-4i)} {(4i)(-4i)} = \frac{-28i-12i*i}{-16i*i}=\frac{-28i+12}{16} =\frac{ -7i+3 }{4} =\frac{3}{4}-\frac{7}{4}i
$
}}$$

7. 1 / a+2i = $$\small{\text{
$
\frac{1} {a+2i} = \frac{1*(a-2i)} {(a+2i)(a-2i)} = \frac{ a-2i }{a^2-4i*i}=\frac{a-2i}{a^2+4} =\frac{a}{a^2+4}-\frac{2}{a^2+4}i
$
}}$$

Thanks, heureka......that's a lot of work for just 3 points !!!!