Question

Please help.. wite complex number in standard form: \[\frac{ 5+4i }{ -9i }\]

Answer 1

If you have a complex number:
\[z=x+iy\]
With x and y real then you define division by complex numbers as multiplying top and bottom by the complex conjugate defined as:
\[z^*=x-iy\]
Please also note that:
\[zz^*=x^2+y^2\]
Therefore division is defined as:
\[\frac{w}{z}=\frac{w z^*}{z z^*}=\frac{w z^*}{x^2+y^2}\]
So we have:\[\frac{5+4i}{-9i}=\frac{(5+4i)(+9i)}{(-9i)(+9i)}=\frac{45i-36}{81}=\frac{5i-4}{9}\]

Answer 2

Where if we let z=x+iy then x=0 for the denominator.