Question

Prove that $(1+\cos(\theta)-i\sin(\theta))^{n} =2^{n}\cos^{n}(\frac{\theta}{2})(\cos(\frac{n\theta}{2})-i\sin((\frac{n\theta}{2}))$

score 382 · Answer 1 · 2026-04-16 19:58:01

Prove that $(1+\cos(\theta)-i\sin(\theta))^{n} =2^{n}\cos^{n}(\frac{\theta}{2})(\cos(\frac{n\theta}{2})-i\sin((\frac{n\theta}{2}))$

score 157 · Answer 2 · 2026-03-26 00:53:47

157

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List Question

Prove that $(1+\cos(\theta)-i\sin(\theta))^{n} =2^{n}\cos^{n}(\frac{\theta}{2})(\cos(\frac{n\theta}{2})-i\sin((\frac{n\theta}{2}))$

what is the value of $\binom{n}{1}+\binom{n}{4}+\binom{n}{7}+\binom{n}{10}+\binom{n}{13}+\dots$

Prove that the limit $\displaystyle\lim_{z\to 0} \frac{|z|^{2a}+i(\operatorname{Re}(z))^a}{z},\ 0<a<1$ does not exist.

Sum of complex numbers with different arguments

How did my professor come up with this equation? Why is 1/i equal to a integral?

Solve a simple complex partial differential equation

find complex matrices

Intuition behind simple complex number loci problems

3blue1brown's complex numbers fundamental video: rotating a point by 30 degrees

Really basic wonderings about $i$.

Prove $|a+b-1| > |ab|$ where $|a|>1$, $a \in \mathbb{C}$, and $b \in (0,1)$.

Prove that the roots of $x^3=1$ add to 0

Check that this transformation is a contraction

Finding the values of this complex number

Cauchy-Riemann equation and differentiability question

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