Argument / Arg / Angle / Phase of complex number Example-1

1. `A=5+6i`
Find Argument / Arg / Angle / Phase of complex number

Solution:
Here `A=5+6i`

For a complex number `z=a+bi`, The argument is `theta=atan(b/a)`

Here, `a=5` and `b=6`

`theta=atan(b/a)` (Since `a>0`)

`:. theta=atan((6)/(5))`

`:. theta=atan(1.2)`

`:. theta=50.1944 ^circ` or `theta=0.8761` rad

2. `A=-2+3i`
Find Argument / Arg / Angle / Phase of complex number

Solution:
Here `A=-2+3i`

For a complex number `z=a+bi`, The argument is `theta=atan(b/a)`

Here, `a=-2` and `b=3`

`theta=atan(b/a)+180` (Since `a<0`)

`:. theta=atan((3)/(-2))+180`

`:. theta=atan(-1.5)+180`

`:. theta=-56.3099+180`

`:. theta=123.6901 ^circ` or `theta=2.1588` rad

3. `A=1-3i`
Find Argument / Arg / Angle / Phase of complex number

Solution:
Here `A=1-3i`

For a complex number `z=a+bi`, The argument is `theta=atan(b/a)`

Here, `a=1` and `b=-3`

`theta=atan(b/a)` (Since `a>0`)

`:. theta=atan((-3)/(1))`

`:. theta=atan(-3)`

`:. theta=-71.5651 ^circ` or `theta=-1.249` rad

This material is intended as a summary. Use your textbook for detail explanation.
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1. Example-1