Problem solver step

Question

Solve the incorrectly and describe the mistake corrcet answer. (5-3)(2+7i)

step 1: 10+35i-6i-21i²

step 2: 10+29i-21i¹

step 3: 10+29i-21

step 4: -11+29i

Answer 1

(5-3i)(2+7i) = 10 -6i +35i - 21i^2 = 10+35i -6i -21i^2

the 1st step is correct, although it could have gone further, combined like terms and expand i^2 to get 10+29i+21 = 31+29i

step 2 has i^1 when it should have written i^2 (but the problem itself is missing an i. It has (5-3) for the 1st factor not (5-3i). that seems to be a typo. but i^1 would be correct if it's not a typo for 3 rather than 3i in the 1st factor. IF the problem really is (5-3)(2+7i) then it equals 2(2+7i) = 4+14i

step 3 would be correct if it has +21 instead of -21

step 4 has the 29i term correct. but it has the same mistake as step 3 in calculating -21 (when +21 is correct) then combining -21 with 10 to get -11

7i times -3i = -21i^2 =-21(-1) = +21, as i^2 = -1