Express as a complex number in simplest a+bi form:start fraction, 13, plus, 7, i, divided by, minus, 3, minus, 10, i, end fraction−3−10i13+7i​

To express the given expression in the simplest a+bi form, we need to follow these steps:

1. Write down the given expression: (13 + 7i) / (-3 - 10i)

2. Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number changes the sign of the imaginary part. So, the conjugate of -3 - 10i is -3 + 10i.

3. Multiply: [(13 + 7i) * (-3 + 10i)] / [(-3 - 10i) * (-3 + 10i)]

4. Distribute in the numerator: (-39 + 130i + 21i - 70) / (9 - 100)

5. Simplify the numerator: (-109 + 151i) / -91

6. Divide the real and imaginary parts of the numerator by the denominator separately: -109/-91 + 151i/-91

7. Simplify to get the answer in a+bi form: 1.2 - 1.66i