Question

express each of the complex number is (1-i)^4 in the form of (a+ib)

Answer 1

solution:

$(1-i)^4\\</p><p>=((1-i)^2)^2\\</p><p>=(1-i)^2(1-i)^2\\</p><p>using (a-b)^2=a^2+b^2-2ab\\</p><p>=(1^2+i^2-2\times 1\times i)(1^2+i^2-2\times1\times i)\\</p><p>=(1+i^2-2i)(1+i^2-2i)\\</p><p>(putting i^2= -1)\\</p><p>=(1-1-2i)(1-1-2i)\\</p><p>=(0-2i)(0-2i)\\</p><p>=(-2i)(-2i)\\</p><p>=4i^2\\</p><p>putting i^2= -1\\</p><p>=4i^2\\</p><p>=4\times -1\\</p><p>=-4\\</p><p>=-4+0\\</p><p>=-4+0i$

Answer 2

Hii I will help you ✌️

Refer to the attachment ✌️