Simplify the expression to a + bi form

Question

sqrt(36) + sqrt(-128)-sqrt(16)+sqrt(-98)

Answer 1

I will only use positive roots to illustrate the procedure.

√36 + √-128 - √16 + √-98

6 + √64 • -2 - 4 + √49 • -2 (• is multiplication operator)

6 + 8√-2 - 4 + 7√-2 ( taking square roots of 64 and 49)

6 + 8√2 i -4 7√2 i (remember √-2 = √2 • -1 = √2 • √-1 =√2 i)

6 -4 +8√2 i + 7√2i (combine integers and simplify the imaginary terms)

2 + 15 •√2 i (final result in a + bi form)

Answer 2

sqr36 = 6

sqrt(-128) = 8isqr2

sqr16 = 4

sqrt(-98) = 7isqr2

sum then all gives 10 +15isqr2 or 10 +15(sqr2)i

a=10, b =15sqr2

for the a+bi form