Final answer:
To express (7+i)² in standard form a+bi, it needs to be expanded to 49 + 14i -1, which simplifies to 48 + 14i when considering i² = -1.
Step-by-step explanation:
To write the expression (7+i)² in standard form a+bi, first, apply the exponent to the binomial by using the formula (a+b)² = a² + 2ab + b². Therefore, we square the real part, multiply the real and imaginary parts by 2, and square the imaginary part. (7+i)² = (7²) + 2(7)(i) + (i²) = 49 + 14i + (i²). Since i² is defined as -1, the expression becomes: = 49 + 14i - 1
= 48 + 14i. This is the expression in the standard form a+bi, where a is 48 and b is 14. Always remember to simplify the expression and check if it is reasonable.