Consider the equation. z=√2√1+√3i The equation can be written as, z‌‌=√2+2√3i ‌‌=√(√3+i)2 ‌‌=±(√3+i) since z lies in the third quadrant z=−√3−i Hence, |z|‌‌=√(−√3)2+(−1)2 ‌‌=√3+1 ‌‌=√4 ‌‌=2 And tan‌θ‌‌=|‌