Question Type 2: Multiplying by a conjugate Bootcamps

Find the conjugate of $4+3i$ and compute $(4+3i)(4-3i)$.

Express $\dfrac{1}{4+3i}$ in the form $a+bi$.

Compute $\dfrac{1}{4+3i}+\dfrac{1}{4-3i}$.

Compute $\dfrac{1}{4+3i}-\dfrac{1}{4-3i}$.

Simplify $\dfrac{4+3i}{4-3i}$ to the form $a+bi$.

Evaluate $\dfrac{2}{4+3i}+\dfrac{3}{4-3i}$ in the form $a+bi$.

Write $\dfrac{7+5i}{4+3i}$ in the form $a+bi$.

Simplify $\dfrac{1}{(4+3i)^2}$ to the form $a+bi$.

Find the real number $x$ such that $\dfrac{x+2i}{4+3i}$ is purely real.

Simplify $\dfrac{7-2i}{4+3i}+\dfrac{7+2i}{4-3i}$ to the form $a+bi$.

Let $z=4+3i$. Find the complex number $w$ with $|w|=1$ such that $wz$ is real and positive.