Question
Download Solution PDFFind the modulus of z = (1 - i)4 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- i2 = - 1
- If z = x + iy then \(|z| = \sqrt{x^2 + y^2}\)
CALCULATION:
Given: z = (1 - i)4 First let's simplify the expression (1 - i)4
⇒ (1 - i)2 = 1 + i2 - 2i
As we know that, i2 = - 1
⇒ (1 + i)2 = -2i
Since (1 - i)4 = (1 - i)2 × (1 - i)2 we get:
⇒ (1 + i)4 = (-2i)2 = - 4
⇒ z = - 4 + 0i
As we know that, if z = x + iy then \(|z| = \sqrt{x^2 + y^2}\)
Here, x = - 4 and y = 0
⇒ \(|z| = \sqrt{(-4)^2 + 0^2} = \pm 4\)
As we know that, |z| denotes the distance between origin and z in the argand plane. So, |z| cannot be negative
⇒ |z| = 4
Hence, correct option is 2.
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