Question

Find the modulus and principal value of argument of
cos squre a + i sin 2a, where - a <a $ 1.
​

Answer 1

Step-by-step explanation:

Let 1=rcosθ,1=rsinθ

Squaring and adding these relations, we get r

2

(cos

2

θ+sin

2

θ)=1

2

+(−1)

2

=2.

Then cosθ=

2

1

,sinθ=

2

−1

,

The value of θ between-π and π which satisfies these equations in −(π/4) Thus ∣1−i∣=r=

2

and arg(1−i)=−(π/4).