Question

Divide. a.1 − 2i/2i b. 5 − 2i/5 + 2i c.√3 − 2i/−2 − √3i

Answer 1

Answer:

(a) \frac{-1i}{2}-1[/tex]

(b) $\frac{20i+21}{29}$

(c) i

Step-by-step explanation:

We have to perform division

(a) $\frac{1-2i}{2i}$

So after division

$\frac{1-2i}{2i}=\frac{1}{2i}-\frac{2i}{2i}=\frac{-1i}{2}-1$

(b) We have given expression $\frac{5-2i}{5+2i}$

After rationalizing $\frac{5-2i}{5+2i}\times \frac{5-2i}{5-2i}=\frac{(5-2i)^2}{25+4}=\frac{25+4i^2+20i}{29}=\frac{20i+21}{29}$

(c) We have given expression $\frac{\sqrt{3}-2i}{-2-\sqrt{3i}}$

After rationalizing

$\frac{\sqrt{3}-2i}{-2-\sqrt{3i}}\times \frac{-2+\sqrt{3i}}{-2+\sqrt{3i}}=\frac{-2\sqrt{3}+7i+2\sqrt{3}}{7}=\frac{7i}{7}=i$