Question

2(cos 45° + i sin 45°) in rectangular form.

a) 1 + i
b) √2 + i√2
c) 1 + i√3
d) √2 + i

Answer 1

By multiplying the trigonometric components cos 45° and sin 45° by 2, we convert the expression 2(cos 45° + i sin 45°) into rectangular form as √2 + i√2, corresponding to option b.

Step-by-step explanation:

We are tasked with converting 2(cos 45° + i sin 45°) into rectangular form. To do this, we can use the fact that cos 45° and sin 45° both equal √2/2.

When we apply these values:

• cos 45° = √2/2
• sin 45° = √2/2

We can multiply both by 2 to convert the expression:

• 2 * (√2/2) = √2
• 2 * (i √2/2) = i√2

Therefore, when we combine these results, the expression in rectangular form is √2 + i√2, which corresponds to option b.