Use the properties of complex numbers to simplify completely (7√−64)+(6+3i).(1 point)
Responses
8i
8 i
1−5i
1 minus 5 i
13+11i
13 plus 11 i
13−5i
To simplify the expression (7√-64) + (6+3i), we start by simplifying the square root of -64 using the property √-1 = i:
√-64 = √(-1 * 64) = √(-1) * √(64) = i * 8 = 8i
Now we substitute this value back into the expression:
(7√-64) + (6+3i) = 7(8i) + (6+3i)
Next, we distribute the 7 and simplify the expression:
= 56i + (6+3i) = 56i + 6 + 3i
Combine like terms:
= (56i + 3i) + 6 = 59i + 6
Therefore, the simplified expression is 59i + 6.