Question

Let z = 1 + i, then | z | = ________. (a)
(b) 2 (c) 2 (d) 0 (ii) Represent the above complex number z in the polar form.​

Answer 1

(i) Given ,

z = 1 + i

$∴ |z| = \sqrt{ {1}^{2} + 1 ^{2} } \\ = \sqrt{2}$

(ii) This imaginary number is represented by the point (1,1) , which lies in the first quadrant of the XY- plane .

So, amp(z) = ϴ = α

Where, tanα = |1|/|1| = |1/1| = |1| = 1 = tan45⁰

∵ tanα= tan45⁰

→ α = 45⁰

∴ ϴ = α = 45⁰

Again r = |z| = $\bold{\sqrt{ {1}^{2} + 1 ^{2} } \:\: = \:\: \sqrt{2} }$

∴ Polar form of the complex number

= r(cosϴ + i.sinϴ)

= √2 (cos45⁰ + i.sin45⁰ )