<s>[INST] How to put $\frac{1}{\cos\theta - j\sin \theta}$ in the form $a+jb$? ($j^2=-1$) I am new to complex numbers and am having trouble putting them in the form $a+jb$ (or $a+bi$) How would I go about putting this expression in the form $a+jb$?
$$\frac{1}{\cos\theta - j\sin \theta}$$
 [/INST] $$\frac{1}{\cos \theta - j \sin \theta}=\frac{\cos \theta + j \sin \theta}{(\cos \theta - j \sin \theta)(\cos \theta + j \sin \theta)}=\frac{\cos \theta+j \sin \theta}{\cos^{2}\theta-j^2 \sin^2 \theta}=\frac{\cos \theta + j \sin \theta}{\cos^2 \theta - (-1)\sin^2 \theta}=\frac{\cos \theta + j \sin \theta}{\cos^2 \theta + \sin^2 \theta}=\frac{\cos \theta + j \sin \theta}{1}=\cos \theta + j \sin \theta$$
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