Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Complex Numbers, Exercise 4: EXERCISE 11B

Find the quadratic equation that has the root $\alpha =-7i , \beta =7i$

Find the quadratic equation that has the root $\alpha =1+5i, \beta =1-5i$

Find the quadratic equation that has the root $\alpha =2-3i, \beta =2+3i$

Find the quadratic equation that has the root $\alpha =-\frac{5}{2}-\frac{\sqrt{31}}{2}i, \beta =-\frac{5}{2}+\frac{\sqrt{31}}{2}i$

Find the complex number $z$ satisfying the equation $z+4=3iz*$. Give your answer in the form $x+\mathrm{i}y,$ where $x$ and $y$ are real.

Find the complex number $u$, given that $u(3-5i)=13+i$

$z=5+i\sqrt{3}$ is a root of a quadratic equation. Find this quadratic equation.

In an electrical circuit, the voltage (volts), current (amperes) and impedance (ohms) are related by the equation
voltage = current $\times$ impedance
The voltage in a particular circuit is $240 \mathrm{V}$ and the impedance is $48+36i$ ohms.
Find the current.