Exercise 190Algebra › Complex numbersL1Added 31 Oct 2026 A power of 1 + i #complex numbers StatementCompute (1+i)20(1+i)^{20}(1+i)20. HintCompute (1+i)2(1+i)^2(1+i)2 first. Show solutionHide solutionSolutionWe have (1+i)2=1+2i+i2=2i(1+i)^2=1+2i+i^2=2i(1+i)2=1+2i+i2=2i. Therefore(1+i)20=((1+i)2)10=(2i)10=210 i10=1024⋅(i2)5=1024⋅(−1)5=−1024.(1+i)^{20}=\left((1+i)^2\right)^{10}=(2i)^{10}=2^{10}\,i^{10}=1024\cdot(i^2)^5=1024\cdot(-1)^5=-1024.(1+i)20=((1+i)2)10=(2i)10=210i10=1024⋅(i2)5=1024⋅(−1)5=−1024.