Question

Simplify the given expression below 4/3-2i

a. 4/13
b. 16/13
c. 12+8i/13
d. 12-8i/13

Answer 1

The correct answer is
`(4)/(3-2i)=(12)/(13)+i(8)/(13)`

Steps:

`\mathrm{Multiply\:by\:the\:conjugate}\:(3+2i)/(3+2i), =(4\left(3+2i\right))/(\left(3-2i\right)\left(3+2i\right))`

`\left(3-2i\right)\left(3+2i\right)=13, =(4\left(3+2i\right))/(13)`

`\mathrm{Rewrite\:}(4\left(3+2i\right))/(13)\mathrm{\:in\:standard\:complex\:form:\:}(12)/(13)+(8)/(13)i`

`=(12)/(13)+(8)/(13)i`