Question

ASAP!! HELP!!!
1) Express $\dfrac{30+19i}{4+9i}$ in the form $a + bi$, where $a$ and $b$ are real numbers.

2) For what real number $k$ does the product $(25 + ki)(3+2i)$ equal a real number?

3) What constant must we place in the box below in order to be able to factor the resulting expression into the product of two linear factors:
\[2mn - 16m - 7n + \boxed{\phantom{00}}?\]

4) How many pairs of integers $(b,c)$ satisfy the equation
\[\frac{b + 7}{b + 4} = \frac{c}{9}?\]

THANK YOU!!!

Answer 1

You should put each question somewhere different so anyone can answer it and see it faster

Answer 2

Question:

Express (30 +1 9i)/(4+  9i) in a form a + bi, where a and b are real numbers.

(I could only get the answer for number 1)

Answer:

3 - 2i

Explanation:

The conjugate of 4+9i is 4-9i. Multiplying the numerator and denominator by 4-9i, we get