Question

Express each of the following in a+bi form. a)(13 +4i)+(7 +5i)b)(5 − i)−2(1 − 3i)c)(3− i)(4 +7i)d)(3 − i)(4 +7i) − i(5 − i) − 2(1 − 3i)i

Answer 1

a)

`20+9i`

b)

`3+5i`

c)

`19+17i`

d)

`12+10i`

Explanation:

a) The sum/difference of two complex numbers is given by:

`(a\pm bi)+(c\pm di)=a\pm c\pm(b\pm d)i`

so:

`(13+4i)+(7+5i)=13+4i+7+5i=20+9i`

b) Using the previous property and the distributive property:

`(5-i)-2*(1-3i)=5-i-2+6i=3+5i`

c)

Using a process similar to the previous one and taking into account that:

`i=√(-1)`

`(3-i)(4+7i)=12+21i-4i+7=19+17i`

d) Using everything we used in the previous problems:

`(3-i)(4+7i)-i(5-i)-2(1-3i)i=19+17i-5i-1-2i-6=12+10i`