Express the given complex number in the form displaystyle a-ib- left- 1-i right- - 4 -

Question

Toppr Admin · Accepted Answer

-1-x2212-i-4-1-x2212-i-2-2-12-i2-x2212-2i-2-1-x2212-1-x2212-2i-2-x2212-2i-2-x2212-2i-xD7-x2212-2i-4i2-x2212-4-x2235-i2-x2212-1-a-ib- where a-x2212-4- and b-0

Express the given complex number in the form $a + i b :$ ${(1 - i)}^{4}$

${(1 - i)}^{4} = {[{(1 - i)}^{2}]}^{2}$
$= {[1^{2} + i^{2} - 2 i]}^{2}$
$= {[1 - 1 - 2 i]}^{2}$
$= {(- 2 i)}^{2}$
$= (- 2 i) \times (- 2 i)$
$= 4 i^{2} = - 4, [∵ i^{2} = - 1]$
$= a + i b$ , where $a = - 4,$ and $b = 0$

Express the given complex number in the form a+ib:(1−i)4

(1−i)4=[(1−i)2]2=[12+i2−2i]2=[1−1−2i]2=(−2i)2=(−2i)×(−2i)=4i2=−4,[∵i2=−1]=a+ib, where a=−4, and b=0

Express the given complex number in the form $a + i b :$ ${(1 - i)}^{4}$

${(1 - i)}^{4} = {[{(1 - i)}^{2}]}^{2}$
$= {[1^{2} + i^{2} - 2 i]}^{2}$
$= {[1 - 1 - 2 i]}^{2}$
$= {(- 2 i)}^{2}$
$= (- 2 i) \times (- 2 i)$
$= 4 i^{2} = - 4, [∵ i^{2} = - 1]$
$= a + i b$ , where $a = - 4,$ and $b = 0$