Krsna is complete in Himself and can NEVER be alone because He is ALWAYS enjoying with His unlimited expansions.

How Krsna is fully complete within Himself is understood in this way -

Krsna is NEVER alone as one, and has never been alone as one because EVERYTHING is situated in Him as one and simultaneously different from Him.

This means Krsna is "simultaneously" one individual Personality, and at the same time "many Personalities".

He is simultaneously one and different, this means He can NEVER be alone because He is already EVERYTHING and EVERYTHING is always part and parcel of Him.

This is the fullness of Lord Krsna.

This is why Krsna is the Supreme Personality of Godhead and cause of ALL causes. 

Krsna is fully satisfied in Himself, that includes through all of His Visnu-tattva and jiva-tattva expansions that are His parts and parcels.

It is not that Krsna is just in our hearts, Krsna is in all things and origin of everything.

In other words, Krsna is NEVER alone just like the Sun-disc can never be alone due to the presence of the surrounding sun-rays that are part and parcel of the Sun-disc.

Krsna is compared to the Sun-disc and the different types of living entities are compared to the sun-rays.

The Sun-disc and the sun-rays cannot exist without each other just like Krsna and the living entities cannot exist without each other meaning Krsna is always surrounded by His parts and parcels.

Krsna IS the Supreme Lord and is simultaneously one with all that there is, but also independent from His expansions, yet Kṛṣṇa is NEVER be alone!

Krsna's eternal consort Srimati Rādhārāṇī is the manifestation of the pleasure potency of Krsna and represents His internal potency.

Guest - "Srila Prabhupāda, are we expansions of Rādhā?"

Srila Prabhupada - "No. Rādhā is the internal potency, we are marginal potency. Of course, originally, in that sense, everything is Kṛṣṇa's expansion. Sarvaṁ khalv idaṁ brahma. But even there are expansions... That is the difference between Māyāvāda philosophy and Vaiṣṇava philosophy.

Caitanya Mahāprabhu teaches acintya bhedābheda. We are always simultaneously one and different. Always. We should remember. We are expansion of Kṛṣṇa, we are expansion of Rādhā also because Rādhā is also expansion of Kṛṣṇa. But still, different. That is our philosophy - 

"One and different simultaneously - Acintya bhedābheda".

Caitanya Mahāprabhu's philosophy is "inconceivable simultaneously one and different". This is explained in the Seventh Chapter of Bhagavad-gītā. The energies and the energetic is the same. Śakti-śaktimator abheda.

Just like sun and the sunshine, they are the same. There is no difference. But the molecules of the sunshine particles, that is not equal to the sun. 

These truths we shall always remember. Acintyāḥ khalu ye bhāvāḥ. Therefore these are inconceivable. We are simultaneously one with Kṛṣṇa and Rādhā, and at the same time different". (Lecture on BG 4.5 -- Montreal, June 10, 1968)

Srila Prabhupada - "Rādhā and Kṛṣṇa are "one and the same", but They have assumed two bodies. Thus They enjoy each other, tasting the mellows of love. The two transcendentalists Rādhā and Kṛṣṇa are a puzzle to materialists. 

The description of Rādhā and Kṛṣṇa from the diary of Śrīla Svarūpa Dāmodara Gosvāmī is a condensed explanation, but one needs great spiritual insight to understand the mystery of these two personalities.

One is enjoying in two.

Śrī Kṛṣṇa is the potent factor, and Śrīmatī Rādhārāṇī is the internal potency. According to Vedānta philosophy, there is no difference between the potent and the potency; they are identical. We cannot differentiate between one and the other, any more than we can separate fire from heat.

Everything in the Absolute is inconceivable in relative existence. Therefore in relative cognizance it is very difficult to assimilate this truth of the oneness between the potent and the potency.

The philosophy of inconceivable oneness and difference propounded by Lord Caitanya is the only source of understanding for such intricacies of transcendence.

In fact, Rādhārāṇī is the internal potency of Śrī Kṛṣṇa, and She eternally intensifies the pleasure of Śrī Kṛṣṇa. Impersonalists cannot understand this without the help of a mahā-bhāgavata devotee.

The very name “Rādhā” suggests that Śrīmatī Rādhārāṇī is eternally the topmost mistress of the comforts of Śrī Kṛṣṇa. As such, She is the medium transmitting the living entities’ service to Śrī Kṛṣṇa.

Devotees in Vṛndāvana therefore seek the mercy of Śrīmatī Rādhārāṇī in order to be recognized as loving servitors of Śrī Kṛṣṇa". (Caitanya Caritamrita Adi 4.56, Translation and Purport)

Srila Prabhupada - "When Krsna wants to be attracted by a woman, He has to create such a woman from His own energy. That woman is Rādhārāṇī". (Srimad Bhagavatam Canto 3 Chapter 31 text 38 Purport)

Krsna divided Himself into "two" so He could experience loving exchanges. 

For even Krsna, love can NEVER exist when there is just "one", there MUST be His expansions like Srimati Radharani and His Visnu-tattva and jiva-tattva expansions.

To experience loving exchanges and emotions with a women, Krsna divided Himself into two, Srimati Radharani and Krsna.

Krsna wanted to experience loving emotions and affection with a women, this is why He divided Himself into "two" - Radha and Krsna, just so He could experience those loving exchanges.

Madhudviṣa Swami - "Śrīla Prabhupāda, you spoke of inferior energy and superior energy. Those are two general categories. Are there other categories of energies besides that, and specifically how could we understand Śrīmatī Rādhārāṇī Is She?"

Srila Prabhupāda - "She is spiritual energy".

Madhudviṣa Swami - "But is She jīva-bhūta or?"

Srila Prabhupada - "No, no, no. She is Kṛṣṇa. If everything is Kṛṣṇa and Rādhārāṇī is not Kṛṣṇa, what is that? Kṛṣṇa. He (She) is Kṛṣṇa. She is the Kṛṣṇa's pleasure potency".

Madhudviṣa Swami - "She is not jīva?"

Srila Prabhupada - "No, no, no. She is Kṛṣṇa. Kṛṣṇa divided Himself into His energy and Himself. That energy, original spiritual energy, is Rādhārāṇī. That is stated by Jīva Gosvāmī. Rādhā kṛṣṇa-praṇaya-vikṛtir hlādinī śaktir asmāt. When Kṛṣṇa wants pleasure, He cannot accept the inferior energy. 

The same superior energy, Kṛṣṇa, is divided into two. That is Rādhā and Kṛṣṇa. And again, when they unite, that is Caitanya Mahāprabhu. Divided, they are Rādhā and Kṛṣṇa, and united, Caitanya Mahāprabhu. 

Śrī-kṛṣṇa-caitanya rādhā-kṛṣṇa nahe anya. Anya means another. 

So Śrī Kṛṣṇa Caitanya is combination of Rādhā and Kṛṣṇa. And when they are divided into two, that is Rādhā and Kṛṣṇa. This is the purport. Rādhā kṛṣṇa-praṇaya-vikṛtir hlādinī śaktir asmād ekātmānāv api bhuvi purā deha-bhedaṁ gatau tau, śrī-caitanyākhyaṁ prakaṭam adhunā tad-dvayaṁ caikyam āptam [Cc. Ādi 1.5]. 

These are the conclusion. Śrī Caitanya Mahāprabhu is Rādhā-Kṛṣṇa combination. But He is playing the part of Rādhārāṇī to understand Kṛṣṇa. This is Caitanya Mahāprabhu. Rādhārāṇī is the chief gopī and all Her young girl friends, they are also gopīs. (Lecture on SB 2.1.1-5 -- Melbourne, June 26, 1974)

"Rādhikā is the transformation of Kṛṣṇa’s love. She is His internal energy called hlādinī". (Caitanya Caritamrita Adi 4.59, Translation)

Srila Prabhupada - "Radharani's mind, senses and body are steeped in love for Kṛṣṇa. She is Kṛṣṇa’s own energy, and She helps Him in His pastimes. 

Śrīmatī Rādhārāṇī is as fully spiritual as Kṛṣṇa. No one should consider Her to be material. 

She is definitely not like the conditioned souls, who have material bodies, gross and subtle, covered by material senses. 

She is all-spiritual, and both Her body and Her mind are of the same spiritual embodiment. 

Because Her body is spiritual, Her senses are also spiritual. Thus Her body, mind and senses fully shine in love of Kṛṣṇa. 

She is the personified hlādinī-śakti (the pleasure-giving energy of the Lord’s internal potency), and therefore She is the only source of enjoyment for Śrī Kṛṣṇa.

Śrī Kṛṣṇa cannot enjoy anything that is internally different from Him. 

Therefore Rādhā and Śrī Kṛṣṇa are identical. The sandhinī portion of Śrī Kṛṣṇa’s internal potency has manifested the all-attractive form of Śrī Kṛṣṇa, and the same internal potency, in the hlādinī feature, has presented Śrīmatī Rādhārāṇī, who is the attraction for the all-attractive. 

No one can match Śrīmatī Rādhārāṇī in the transcendental pastimes of Śrī Kṛṣṇa". (Caitanya Caritamrta Adi 4.71, Translation and Purport)

"Just as the fountainhead, Lord Kṛṣṇa, is the cause of all incarnations, so Śrī Rādhā is the cause of all these consorts". (Caitanya Caritamrita Adi 4.76, Translation)

"Rādhā is the one who gives pleasure to Govinda, and She is also the enchantress of Govinda. She is the be-all and end-all of Govinda, and the crest jewel of all His consorts". (Caitanya Caritamrita Adi 4.82, Translation)

"The transcendental goddess Śrīmatī Rādhārāṇī is the direct counterpart of Lord Śrī Kṛṣṇa. 

She is the central figure for all the goddesses of fortune. She possesses all the attractiveness to attract the all-attractive Personality of Godhead. She is the primeval internal potency of the Lord". (Caitanya Caritamrta Adi 4.83, Translation)

Srila Prabhupada - "When Krsna wants to be attracted by a woman, He has to create such a woman from His own energy. That woman is Rādhārāṇī. 

It is explained by the Gosvāmīs that Rādhārāṇī is the manifestation of the pleasure potency of the Supreme Personality of Godhead. 

When the Supreme Lord wants to derive transcendental pleasure, He has to create a woman from His internal potency and that women is Srimati Radharani" (Srimad Bhagavatam Canto 3 Chapter 31 text 38, Purport)+^+