A) For ab>0
⇒a>0,b>0 or a<0,b<0
⇒z is 1st or 3rd quadrant
⇒⎧⎪
⎪⎨⎪
⎪⎩tan−1baa>0,b>0tan−1ba−πa<0,b<0
B) For ab<0
⇒a<0,b>0 or a>0,b<0
⇒z in 2nd or 4th quadrant
⇒⎧⎪
⎪⎨⎪
⎪⎩π−tan−1baa<0,b>0−tan−1baa>0,b<0
C) a2+b2=0⇒a=b=0
⇒ argument is not defined
D) ab=0⇒a=0 or b=0
⇒⎧⎪
⎪⎨⎪
⎪⎩tan−1b0=π2a=0tan−10a=0b=0