R S Aggarwal Solutions for Exercise 2: EXERCISE 5B

Simplify each of the following and express it in the form $a+ib$:

$\left(3+4i\right)\left(2-3i\right)$

The modulus of the following: $(1+2i)(i-1)$ is of the form $\sqrt{a}$, then $a=$

The multiplicative inverse of $(1-\sqrt{3}i)$ is of the form $\frac{a+i\sqrt{b}}{c}$, then $b=$

The multiplicative inverse of $(2+5 i)$ is of the form of $\frac{a-ib}{c}$, then $b=$

The multiplicative inverse of $\frac{(2+3i)}{(1+i)}$ is of the form $\frac{a-ib}{c}$ then $a=$

Find the multiplicative inverse of the following:

$\frac{(1+i)(1+2i)}{(1+3i)}$

If $\left(\frac{z-1}{z+1}\right)$ is purely an imaginary number and $z\ne -1$ then find the value of $\left|z\right|$.

Find the complex number $z$ for which $\left|z\right|=z+1+2i$.