Solution Use the standard form. If z=x+iyz=x+iyz=x+iy and y≠0y\neq 0y=0 then: z=±(∣z∣+x2+i sgn(y)∣z∣−x2)\sqrt{z}=\pm\left(\sqrt{\frac{|z|+x}{2}}+i\,\operatorname{sgn}(y)\sqrt{\frac{|z|-x}{2}}\right)z=±(2∣z∣+x+isgn(y)2∣z∣−x) (i) z=−7−24iz=-7-24iz=−7−24i ∣z∣=25⇒z=±(3−4i)|z|=25\Rightarrow \sqrt{z}=\pm(3-4i)∣z∣=25⇒z=±(3−4i) (ii) z=8−6iz=8-6iz=8−6i ∣z∣=10⇒z=±(3−i)|z|=10\Rightarrow \sqrt{z}=\pm(3-i)∣z∣=10⇒z=±(3−i) (iii) z=−15−36iz=-15-36iz=−15−36i ∣z∣=39⇒z=±(23−33 i)|z|=39\Rightarrow \sqrt{z}=\pm\left(2\sqrt{3}-3\sqrt{3}\,i\right)∣z∣=39⇒z=±(23−33i) (iv) z=119+120iz=119+120iz=119+120i ∣z∣=169⇒z=±(12+5i)|z|=169\Rightarrow \sqrt{z}=\pm(12+5i)∣z∣=169⇒z=±(12+5i)